Jose Luis Mancilla-Aguilar - Academia.edu (original) (raw)

Papers by Jose Luis Mancilla-Aguilar

2017 XVII Workshop on Information Processing and Control (RPIC), 2017

How to bound the state vector trajectory of a nonlinear system in a way so that the obtained boun... more How to bound the state vector trajectory of a nonlinear system in a way so that the obtained bound be of practical value is an open problem. If some norm is employed for bounding the state vector trajectory, then this norm should be carefully selected and the state vector components suitably scaled. In addition, practical applications usually require separate bounds on every state variable. Bearing this context in mind, we develop a novel componentwise bounding procedure applicable to both real and complex nonlinear systems with additive disturbances. A bound on the magnitude of the evolution of each state variable is obtained by computing a single trajectory of a well-specified “bounding” system constructed from the original system equations and the available disturbance bounds. The bounding system is shown to have highly desirable properties, such as being monotone and positive. We provide preliminary results establishing that key stability features are preserved by the bounding s...

Nonlinear Analysis: Hybrid Systems, 2020

We provide novel sufficient conditions for stability of nonlinear and time-varying impulsive syst... more We provide novel sufficient conditions for stability of nonlinear and time-varying impulsive systems. These conditions generalize, extend, and strengthen many existing results. Different types of input-to-state stability (ISS), as well as zero-input global uniform asymptotic stability (0-GUAS), are covered by employing a twomeasure framework and considering stability of both weak (decay depends only on elapsed time) and strong (decay depends on elapsed time and the number of impulses) flavors. By contrast to many existing results, the stability state bounds imposed are uniform with respect to initial time and also with respect to classes of impulse-time sequences where the impulse frequency is eventually uniformly bounded. We show that the considered classes of impulse-time sequences are substantially broader than other previously considered classes, such as those having fixed or (reverse) average dwell times, or impulse frequency achieving uniform convergence to a limit (superior or inferior). Moreover, our sufficient conditions are not more restrictive than existing ones when particularized to some of the cases covered in the literature, and hence in these cases our results allow to strengthen the existing conclusions.

Automatica, 2020

Suitable continuity and boundedness assumptions on the function f defining the dynamics of a time... more Suitable continuity and boundedness assumptions on the function f defining the dynamics of a time-varying nonimpulsive system with inputs are known to make the system inherit stability properties from the zero-input system. Whether this type of robustness holds or not for impulsive systems was still an open question. By means of suitable (counter)examples, we show that such stability robustness with respect to the inclusion of inputs cannot hold in general, not even for impulsive systems with time-invariant flow and jump maps. In particular, we show that zero-input global uniform asymptotic stability (0-GUAS) does not imply converging input converging state (CICS), and that 0-GUAS and uniform bounded-energy input bounded state (UBEBS) do not imply integral input-to-state stability (iISS). We also comment on available existing results that, however, show that suitable constraints on the allowed impulse-time sequences indeed make some of these robustness properties possible.

Automatica, 2020

For time-invariant (nonimpulsive) systems, it is already well-known that the input-to-state stabi... more For time-invariant (nonimpulsive) systems, it is already well-known that the input-to-state stability (ISS) property is strictly stronger than integral input-to-state stability (iISS). Very recently, we have shown that under suitable uniform boundedness and continuity assumptions on the function defining system dynamics, ISS implies iISS also for time-varying systems. In this paper, we show that this implication remains true for impulsive systems, provided that asymptotic stability is understood in a sense stronger than usual for impulsive systems.

Automatica, 2019

For time-invariant systems, the property of input-to-state stability (ISS) is known to be strictl... more For time-invariant systems, the property of input-to-state stability (ISS) is known to be strictly stronger than integral-ISS (iISS). Known proofs of the fact that ISS implies iISS employ Lyapunov characterizations of both properties. For time-varying and switched systems, such Lyapunov characterizations may not exist, and hence establishing the exact relationship between ISS and iISS remained an open problem, until now. In this paper, we solve this problem by providing a direct proof, i.e. without requiring Lyapunov characterizations, of the fact that ISS implies iISS, in a very general time-varying and switched-system context. In addition, we show how to construct suitable iISS gains based on the comparison functions that characterize the ISS property, and on bounds on the function f defining the system dynamics. When particularized to time-invariant systems, our assumptions are even weaker than existing ones. Another contribution is to show that for time-varying systems, local Lipschitz continuity of f in all variables is not sufficient to guarantee that ISS implies iISS. We illustrate application of our results on an example that does not admit an iISS-Lyapunov function.

Systems & Control Letters, 2017

Stability results for time-varying systems with inputs are relatively scarce, as opposed to the a... more Stability results for time-varying systems with inputs are relatively scarce, as opposed to the abundant literature available for time-invariant systems. This paper extends to time-varying systems existing results that ensure that if the input converges to zero in some specific sense, then the state trajectory will inherit stability properties from the corresponding zero-input system. This extension is non-trivial, in the sense that the proof technique is completely novel, and allows to recover the existing results under weaker assumptions in a unifying way.

IEEE Transactions on Automatic Control, 2017

Most of the existing characterizations of the integral inputto-state stability (iISS) property ar... more Most of the existing characterizations of the integral inputto-state stability (iISS) property are not valid for time-varying or switched systems in cases where converse Lyapunov theorems for stability are not available. This note provides a characterization that is valid for switched and time-varying systems, and shows that natural extensions of some of the existing characterizations result in only sufficient but not necessary conditions. The results provided also pinpoint suitable iISS gains and relate these to supply functions and bounds on the function defining the system dynamics.

Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301), 2002

... State-Norm Estimation of Switched Nonlinear Systems RA Garcia and JL Mancilla-Aguilar Departa... more ... State-Norm Estimation of Switched Nonlinear Systems RA Garcia and JL Mancilla-Aguilar Departamento de MatemLica, Facultad de Ingenieria, Universidad de Buenos Aires Paseo C ob 850, (1063) Buenos Aires, Argentina, e-mail: rgarciaQfi.uba.ar, jmancilQfi.uba.ar Abstract ...

Revista Iberoamericana de Automática e Informática Industrial RIAI, 2008

Systems & Control Letters, 2000

In this paper we present a converse Lyapunov theorem for uniform asymptotic stability of switched... more In this paper we present a converse Lyapunov theorem for uniform asymptotic stability of switched nonlinear systems. Its proof is a simple consequence of some results on converse Lyapunov theorems for systems with bounded disturbances obtained by Lin et al. (SIAM J. Control Optim. 34 (1996) 124-160), once an association of the switched system with a nonlinear system with disturbances is established.

In this paper we obtain the extension of results on input-to-output stability properties of switc... more In this paper we obtain the extension of results on input-to-output stability properties of switched systems to switched systems whose dynamics are described by perturbed forced differential equations and whose outputs are obtained via switched perturbed functions. We also present Lyapunov characterizations of these input-output stability properties, obtained in terms of certain conceptual output functions.

Proceedings of the 36th IEEE Conference on Decision and Control, 1997

ABSTRACT The definitions of π-trajectories of nonnecessary continuous feedback and of s-stability... more ABSTRACT The definitions of π-trajectories of nonnecessary continuous feedback and of s-stability were introduced by Clarke et al. (1996). In this work we prove that a Lipschitz stabilizer is an s-stabilizer, and we give a sufficient condition for the convergence of the π-trajectories of this class of stabilizers to the origin. When the digital implementation of Lipschitz stabilizers is carried out by sampling and zero-order hold (SZH) with nonconstant sampling rate the trajectories of the resulting system are π-trajectories. In consequence these results are an extension of the authors' previous results (1997) related to the digital implementation of feedback stabilization laws of nonlinear continuous time control systems

2018 Argentine Conference on Automatic Control (AADECA)

Most of the existing characterizations of the integral input-to-state stability (iISS) property a... more Most of the existing characterizations of the integral input-to-state stability (iISS) property are not suitable for timevarying or switched (nonlinear) systems. Previous work by the authors has shown that in such cases where converse Lyapunov theorems for stability are not available, iISS-Lyapunov functions may not exist. In these cases, the iISS property can still be characterized as the combination of global uniform asymptotic stability under zero input (0-GUAS) and uniformly bounded energy input-bounded state (UBEBS). This paper shows that such a characterization remains valid for time-varying impulsive systems, under an appropriate condition on the number of impulse times on each finite time interval.

2019 XVIII Workshop on Information Processing and Control (RPIC)

For general time-varying or switched (nonlinear) systems, converse Lyapunov theorems for stabilit... more For general time-varying or switched (nonlinear) systems, converse Lyapunov theorems for stability are not available. In these cases, the integral input-to-state stability (iISS) property is not equivalent to the existence of an iISS-Lyapunov function but can still be characterized as the combination of global uniform asymptotic stability under zero input (0-GUAS) and uniformly bounded energy input-bounded state (UBEBS). For impulsive systems, asymptotic stability can be weak (when the asymptotic decay depends only on elapsed time) or strong (when such a decay depends also on the number of impulses that occurred). This paper shows that the mentioned characterization of iISS remains valid for time-varying impulsive systems, provided that stability is understood in the strong sense.

IEEE Transactions on Automatic Control, 2021

It is shown that impulsive systems of nonlinear, time-varying and/or switched form that allow a s... more It is shown that impulsive systems of nonlinear, time-varying and/or switched form that allow a stable global state weak linearization are jointly input-to-state stable (ISS) under small inputs and integral ISS (iISS). The system is said to allow a global state weak linearization if its flow and jump equations can be written as a (time-varying, switched) linear part plus a (nonlinear) pertubation satisfying a bound of affine form on the state. This bound reduces to a linear form under zero input but does not force the system to be linear under zero input. The given results generalize and extend previously existing ones in many directions: (a) no (dwell-time or other) constraints are placed on the impulse-time sequence, (b) the system need not be linear under zero input, (c) existence of a (common) Lyapunov function is not required, (d) the perturbation bound need not be linear on the input.

2018 Annual American Control Conference (ACC), 2018

In this paper we present a criterion for the uniform global asymptotic stability of switched nonl... more In this paper we present a criterion for the uniform global asymptotic stability of switched nonlinear systems with time/state-dependent switching constraints but with no dwell-time assumptions. This criterion is based on the existence of multiple weak common Lyapunov functions and on a detectability property of a reduced control system.

IEEE Control Systems Letters, 2020

Very recently, it has been shown that the standard notion of stability for impulsive systems, whe... more Very recently, it has been shown that the standard notion of stability for impulsive systems, whereby the state is ensured to approach the equilibrium only as continuous time elapses, is too weak to allow for any meaningful type of robustness in a time-varying impulsive system setting. By strengthening the notion of stability so that convergence to the equilibrium occurs not only as time elapses but also as the number of jumps increases, some facts that are well-established for time-invariant nonimpulsive systems can be recovered for impulsive systems. In this context, our contribution is to provide novel results consisting in rather mild conditions under which stability under zero input implies stability under inputs that converge to zero in some appropriate sense.

IEEE Transactions on Automatic Control, 2020

We provide a Lyapunov-function-based method for establishing different types of uniform input-to-... more We provide a Lyapunov-function-based method for establishing different types of uniform input-to-state stability (ISS) for time-varying impulsive systems. The method generalizes to impulsive systems with inputs the well-established philosophy of assessing the stability of a system by reducing the problem to that of the stability of a scalar system given by the evolution of the Lyapunov function on the system trajectories. This reduction is performed in such a way so that the resulting scalar system has no inputs. Novel sufficient conditions for ISS are provided, which generalize existing results for time-invariant and timevarying, switched and nonswitched, impulsive and nonimpulsive systems in several directions.

IEEE Transactions on Automatic Control, 2019

This paper is concerned with the study of both, local and global, uniform asymptotic stability fo... more This paper is concerned with the study of both, local and global, uniform asymptotic stability for switched nonlinear time-varying (NLTV) systems through the detectability of outputmaps. With this aim the notion of reduced limiting control systems for switched NLTV systems whose switchings verify time/state dependent constraints, and the concept of weakly zerostate detectability for those reduced limiting systems are introduced. Necessary and sufficient conditions for the (global)uniform asymptotic stability of families of trajectories of the switched system are obtained in terms of this detectability property. These sufficient conditions in conjunction with the existence of multiple weak Lyapunov functions, yield a criterion for the (global) uniform asymptotic stability of families of trajectories of the switched system. This criterion can be seen as an extension of the classical Krasovskii-LaSalle theorem. An interesting feature of the results is that no dwell-time assumptions are made. Moreover, they can be used for establishing the global uniform asymptotic stability of switched NLTV system under arbitrary switchings. The effectiveness of the proposed results is illustrated by means of various interesting examples, including the stability analysis of a semi-quasi-Z-source inverter.

2017 XVII Workshop on Information Processing and Control (RPIC), 2017

How to bound the state vector trajectory of a nonlinear system in a way so that the obtained boun... more How to bound the state vector trajectory of a nonlinear system in a way so that the obtained bound be of practical value is an open problem. If some norm is employed for bounding the state vector trajectory, then this norm should be carefully selected and the state vector components suitably scaled. In addition, practical applications usually require separate bounds on every state variable. Bearing this context in mind, we develop a novel componentwise bounding procedure applicable to both real and complex nonlinear systems with additive disturbances. A bound on the magnitude of the evolution of each state variable is obtained by computing a single trajectory of a well-specified “bounding” system constructed from the original system equations and the available disturbance bounds. The bounding system is shown to have highly desirable properties, such as being monotone and positive. We provide preliminary results establishing that key stability features are preserved by the bounding s...

Nonlinear Analysis: Hybrid Systems, 2020

We provide novel sufficient conditions for stability of nonlinear and time-varying impulsive syst... more We provide novel sufficient conditions for stability of nonlinear and time-varying impulsive systems. These conditions generalize, extend, and strengthen many existing results. Different types of input-to-state stability (ISS), as well as zero-input global uniform asymptotic stability (0-GUAS), are covered by employing a twomeasure framework and considering stability of both weak (decay depends only on elapsed time) and strong (decay depends on elapsed time and the number of impulses) flavors. By contrast to many existing results, the stability state bounds imposed are uniform with respect to initial time and also with respect to classes of impulse-time sequences where the impulse frequency is eventually uniformly bounded. We show that the considered classes of impulse-time sequences are substantially broader than other previously considered classes, such as those having fixed or (reverse) average dwell times, or impulse frequency achieving uniform convergence to a limit (superior or inferior). Moreover, our sufficient conditions are not more restrictive than existing ones when particularized to some of the cases covered in the literature, and hence in these cases our results allow to strengthen the existing conclusions.

Automatica, 2020

Suitable continuity and boundedness assumptions on the function f defining the dynamics of a time... more Suitable continuity and boundedness assumptions on the function f defining the dynamics of a time-varying nonimpulsive system with inputs are known to make the system inherit stability properties from the zero-input system. Whether this type of robustness holds or not for impulsive systems was still an open question. By means of suitable (counter)examples, we show that such stability robustness with respect to the inclusion of inputs cannot hold in general, not even for impulsive systems with time-invariant flow and jump maps. In particular, we show that zero-input global uniform asymptotic stability (0-GUAS) does not imply converging input converging state (CICS), and that 0-GUAS and uniform bounded-energy input bounded state (UBEBS) do not imply integral input-to-state stability (iISS). We also comment on available existing results that, however, show that suitable constraints on the allowed impulse-time sequences indeed make some of these robustness properties possible.

Automatica, 2020

For time-invariant (nonimpulsive) systems, it is already well-known that the input-to-state stabi... more For time-invariant (nonimpulsive) systems, it is already well-known that the input-to-state stability (ISS) property is strictly stronger than integral input-to-state stability (iISS). Very recently, we have shown that under suitable uniform boundedness and continuity assumptions on the function defining system dynamics, ISS implies iISS also for time-varying systems. In this paper, we show that this implication remains true for impulsive systems, provided that asymptotic stability is understood in a sense stronger than usual for impulsive systems.

Automatica, 2019

For time-invariant systems, the property of input-to-state stability (ISS) is known to be strictl... more For time-invariant systems, the property of input-to-state stability (ISS) is known to be strictly stronger than integral-ISS (iISS). Known proofs of the fact that ISS implies iISS employ Lyapunov characterizations of both properties. For time-varying and switched systems, such Lyapunov characterizations may not exist, and hence establishing the exact relationship between ISS and iISS remained an open problem, until now. In this paper, we solve this problem by providing a direct proof, i.e. without requiring Lyapunov characterizations, of the fact that ISS implies iISS, in a very general time-varying and switched-system context. In addition, we show how to construct suitable iISS gains based on the comparison functions that characterize the ISS property, and on bounds on the function f defining the system dynamics. When particularized to time-invariant systems, our assumptions are even weaker than existing ones. Another contribution is to show that for time-varying systems, local Lipschitz continuity of f in all variables is not sufficient to guarantee that ISS implies iISS. We illustrate application of our results on an example that does not admit an iISS-Lyapunov function.

Systems & Control Letters, 2017

Stability results for time-varying systems with inputs are relatively scarce, as opposed to the a... more Stability results for time-varying systems with inputs are relatively scarce, as opposed to the abundant literature available for time-invariant systems. This paper extends to time-varying systems existing results that ensure that if the input converges to zero in some specific sense, then the state trajectory will inherit stability properties from the corresponding zero-input system. This extension is non-trivial, in the sense that the proof technique is completely novel, and allows to recover the existing results under weaker assumptions in a unifying way.

IEEE Transactions on Automatic Control, 2017

Most of the existing characterizations of the integral inputto-state stability (iISS) property ar... more Most of the existing characterizations of the integral inputto-state stability (iISS) property are not valid for time-varying or switched systems in cases where converse Lyapunov theorems for stability are not available. This note provides a characterization that is valid for switched and time-varying systems, and shows that natural extensions of some of the existing characterizations result in only sufficient but not necessary conditions. The results provided also pinpoint suitable iISS gains and relate these to supply functions and bounds on the function defining the system dynamics.

Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301), 2002

... State-Norm Estimation of Switched Nonlinear Systems RA Garcia and JL Mancilla-Aguilar Departa... more ... State-Norm Estimation of Switched Nonlinear Systems RA Garcia and JL Mancilla-Aguilar Departamento de MatemLica, Facultad de Ingenieria, Universidad de Buenos Aires Paseo C ob 850, (1063) Buenos Aires, Argentina, e-mail: rgarciaQfi.uba.ar, jmancilQfi.uba.ar Abstract ...

Revista Iberoamericana de Automática e Informática Industrial RIAI, 2008

Systems & Control Letters, 2000

In this paper we present a converse Lyapunov theorem for uniform asymptotic stability of switched... more In this paper we present a converse Lyapunov theorem for uniform asymptotic stability of switched nonlinear systems. Its proof is a simple consequence of some results on converse Lyapunov theorems for systems with bounded disturbances obtained by Lin et al. (SIAM J. Control Optim. 34 (1996) 124-160), once an association of the switched system with a nonlinear system with disturbances is established.

In this paper we obtain the extension of results on input-to-output stability properties of switc... more In this paper we obtain the extension of results on input-to-output stability properties of switched systems to switched systems whose dynamics are described by perturbed forced differential equations and whose outputs are obtained via switched perturbed functions. We also present Lyapunov characterizations of these input-output stability properties, obtained in terms of certain conceptual output functions.

Proceedings of the 36th IEEE Conference on Decision and Control, 1997

ABSTRACT The definitions of π-trajectories of nonnecessary continuous feedback and of s-stability... more ABSTRACT The definitions of π-trajectories of nonnecessary continuous feedback and of s-stability were introduced by Clarke et al. (1996). In this work we prove that a Lipschitz stabilizer is an s-stabilizer, and we give a sufficient condition for the convergence of the π-trajectories of this class of stabilizers to the origin. When the digital implementation of Lipschitz stabilizers is carried out by sampling and zero-order hold (SZH) with nonconstant sampling rate the trajectories of the resulting system are π-trajectories. In consequence these results are an extension of the authors' previous results (1997) related to the digital implementation of feedback stabilization laws of nonlinear continuous time control systems

2018 Argentine Conference on Automatic Control (AADECA)

Most of the existing characterizations of the integral input-to-state stability (iISS) property a... more Most of the existing characterizations of the integral input-to-state stability (iISS) property are not suitable for timevarying or switched (nonlinear) systems. Previous work by the authors has shown that in such cases where converse Lyapunov theorems for stability are not available, iISS-Lyapunov functions may not exist. In these cases, the iISS property can still be characterized as the combination of global uniform asymptotic stability under zero input (0-GUAS) and uniformly bounded energy input-bounded state (UBEBS). This paper shows that such a characterization remains valid for time-varying impulsive systems, under an appropriate condition on the number of impulse times on each finite time interval.

2019 XVIII Workshop on Information Processing and Control (RPIC)

For general time-varying or switched (nonlinear) systems, converse Lyapunov theorems for stabilit... more For general time-varying or switched (nonlinear) systems, converse Lyapunov theorems for stability are not available. In these cases, the integral input-to-state stability (iISS) property is not equivalent to the existence of an iISS-Lyapunov function but can still be characterized as the combination of global uniform asymptotic stability under zero input (0-GUAS) and uniformly bounded energy input-bounded state (UBEBS). For impulsive systems, asymptotic stability can be weak (when the asymptotic decay depends only on elapsed time) or strong (when such a decay depends also on the number of impulses that occurred). This paper shows that the mentioned characterization of iISS remains valid for time-varying impulsive systems, provided that stability is understood in the strong sense.

IEEE Transactions on Automatic Control, 2021

It is shown that impulsive systems of nonlinear, time-varying and/or switched form that allow a s... more It is shown that impulsive systems of nonlinear, time-varying and/or switched form that allow a stable global state weak linearization are jointly input-to-state stable (ISS) under small inputs and integral ISS (iISS). The system is said to allow a global state weak linearization if its flow and jump equations can be written as a (time-varying, switched) linear part plus a (nonlinear) pertubation satisfying a bound of affine form on the state. This bound reduces to a linear form under zero input but does not force the system to be linear under zero input. The given results generalize and extend previously existing ones in many directions: (a) no (dwell-time or other) constraints are placed on the impulse-time sequence, (b) the system need not be linear under zero input, (c) existence of a (common) Lyapunov function is not required, (d) the perturbation bound need not be linear on the input.

2018 Annual American Control Conference (ACC), 2018

In this paper we present a criterion for the uniform global asymptotic stability of switched nonl... more In this paper we present a criterion for the uniform global asymptotic stability of switched nonlinear systems with time/state-dependent switching constraints but with no dwell-time assumptions. This criterion is based on the existence of multiple weak common Lyapunov functions and on a detectability property of a reduced control system.

IEEE Control Systems Letters, 2020

Very recently, it has been shown that the standard notion of stability for impulsive systems, whe... more Very recently, it has been shown that the standard notion of stability for impulsive systems, whereby the state is ensured to approach the equilibrium only as continuous time elapses, is too weak to allow for any meaningful type of robustness in a time-varying impulsive system setting. By strengthening the notion of stability so that convergence to the equilibrium occurs not only as time elapses but also as the number of jumps increases, some facts that are well-established for time-invariant nonimpulsive systems can be recovered for impulsive systems. In this context, our contribution is to provide novel results consisting in rather mild conditions under which stability under zero input implies stability under inputs that converge to zero in some appropriate sense.

IEEE Transactions on Automatic Control, 2020

We provide a Lyapunov-function-based method for establishing different types of uniform input-to-... more We provide a Lyapunov-function-based method for establishing different types of uniform input-to-state stability (ISS) for time-varying impulsive systems. The method generalizes to impulsive systems with inputs the well-established philosophy of assessing the stability of a system by reducing the problem to that of the stability of a scalar system given by the evolution of the Lyapunov function on the system trajectories. This reduction is performed in such a way so that the resulting scalar system has no inputs. Novel sufficient conditions for ISS are provided, which generalize existing results for time-invariant and timevarying, switched and nonswitched, impulsive and nonimpulsive systems in several directions.

IEEE Transactions on Automatic Control, 2019

This paper is concerned with the study of both, local and global, uniform asymptotic stability fo... more This paper is concerned with the study of both, local and global, uniform asymptotic stability for switched nonlinear time-varying (NLTV) systems through the detectability of outputmaps. With this aim the notion of reduced limiting control systems for switched NLTV systems whose switchings verify time/state dependent constraints, and the concept of weakly zerostate detectability for those reduced limiting systems are introduced. Necessary and sufficient conditions for the (global)uniform asymptotic stability of families of trajectories of the switched system are obtained in terms of this detectability property. These sufficient conditions in conjunction with the existence of multiple weak Lyapunov functions, yield a criterion for the (global) uniform asymptotic stability of families of trajectories of the switched system. This criterion can be seen as an extension of the classical Krasovskii-LaSalle theorem. An interesting feature of the results is that no dwell-time assumptions are made. Moreover, they can be used for establishing the global uniform asymptotic stability of switched NLTV system under arbitrary switchings. The effectiveness of the proposed results is illustrated by means of various interesting examples, including the stability analysis of a semi-quasi-Z-source inverter.