E. Fridman - Academia.edu (original) (raw)

Papers by E. Fridman

IEEE Transactions on Automatic Control, 2002

In this note, we combine a new approach for linear timedelay systems based on a descriptor repres... more In this note, we combine a new approach for linear timedelay systems based on a descriptor representation with a recent result on bounding of cross products of vectors. A delay-dependent criterion for determining the stability of systems with time-varying delays is obtained. This criterion is used to derive an efficient stabilizing state-feedback design method for systems with parameter uncertainty, of either the polytopic or the norm-bounded types.

IEEE Transactions on Automatic Control, 2003

A new robust delay dependent stability test is introduced that determines the asymptotic stabilit... more A new robust delay dependent stability test is introduced that determines the asymptotic stability of linear systems with state delays. The parameters of the system are not exactly given. They are known to reside in a given polytope. The test provides an efficient sufficient condition for the stability of the system over the uncertainty polytope. This condition is parameter dependent and it therefore improves previous results that were derived using a single Lyapunov-Krasovskii functional. The stability test is readily extended to provide a criterion for robust stabilization via statefeedback.

Asian Journal of Control, 2008

This paper investigates the robust stability of linear neutral systems with mixed delays and norm... more This paper investigates the robust stability of linear neutral systems with mixed delays and norm-bounded uncertainty. Using new Lyapunov-Krasovskii functionals, less conservative delay-dependent robust stability conditions for such systems in terms of linear matrix inequalities (LMIs) are derived. Numerical examples show that the results obtained in this paper significantly improve the estimate of the stability limit over some existing results in other literature.

International Journal of Control, 2009

Sampled-data H 1 control of linear systems with constant state, control and measurement delays is... more Sampled-data H 1 control of linear systems with constant state, control and measurement delays is considered. The sampling of the controlled input and of the measured output is not assumed to be uniform. The system is modelled as a continuous-time one, where the controlled input and the measurement output have piecewise-continuous delays. The input-output approach to stability and L 2-gain analysis is applied to the resulting system. The discretised Lyapunov functional method is extended to the case of multiple delays, where the Lyapunov functional is complete in one of the delays (in the state) and is simple in the other delays (those in the input and in the output), which are constant. Solutions to the state-feedback and the outputfeedback H 1 control problems are derived in terms of linear matrix inequalities (LMIs).

International Journal of Control, 2005

Robust stability and the guaranteed cost control problem are considered for discrete-time systems... more Robust stability and the guaranteed cost control problem are considered for discrete-time systems with time-varying delays from given intervals. A new construction of Lyapunov-Krasovskii functionals (LKFs), which has been recently introduced in the continuous-time case, is applied. To a nominal LKF, which is appropriate to the system with nominal delays, terms are added that correspond to the system with the perturbed delays and that vanish when the delay perturbations approach zero. The nominal LKF is chosen in the form of the descriptor type and is applied either to the original or to the augmented system. The delayindependent result is derived via the Razumikhin approach. Guaranteed cost state-feedback control is designed. The advantage of the new tests is demonstrated via illustrative examples.

IEEE Transactions on Automatic Control, 2009

It is well known that for linear, uncertain systems, a static output feedback sliding mode contro... more It is well known that for linear, uncertain systems, a static output feedback sliding mode controller can only be determined if a particular triple associated with the reduced order dynamics in the sliding mode is stabilisable. This paper shows that the static output feedback sliding mode control design problem can be solved for a broader class of systems if a known delay term is deliberately introduced into the switching function. Effectively the reduced order sliding mode dynamics are stabilized by the introduction of this artificial delay.

Abstract For linear singularly perturbed system with delay sufficient conditions for stability fo... more Abstract For linear singularly perturbed system with delay sufficient conditions for stability for all small enough values of singular perturbation parameter e are obtained in the general case, when delay and ξ are independent. The sufficient delay-dependent conditions are given in terms of linear matrix inequalities (LMIs) by applying an appropriate Lyapunov-Krasovskii functional. LMIs are derived by using a descriptor model transformation and Park's inequality for bounding cross terms. A memoryless state-feedback stabilizing controller is obtained. Numerical examples illustrate the effectiveness of the new theory.

Proceedings. 1996 IEEE International Workshop on Variable Structure Systems. - VSS'96 -, 2000

The second order relay control systems with delay (S O R C S D) are considered. It is shown that ... more The second order relay control systems with delay (S O R C S D) are considered. It is shown that the average frequency of any oscillatory solution of S O R C S D after a finite time interval becomes a constant. We give Sumcient conditions for the existence of periodic oscillations in S O R C S D for any frequency, and sumcient conditions for the orbital asymptotic stability of periodic oscillations with the minimal (zero) average frequency.

Systems & Control Letters, 2014

ABSTRACT The paper considers a distributed robust estimation problem over a network with directed... more ABSTRACT The paper considers a distributed robust estimation problem over a network with directed topology involving continuous time observers. While measurements are available to the observers continuously, the nodes interact according to a Round-Robin rule, at discrete time instances. The results of the paper are sufficient conditions which guarantee a suboptimal H∞H∞ level of consensus between observers with sampled interconnections.

6th IFAC Symposium on Robust Control Design, 2009, 2009

ABSTRACT The paper considers the observer design problem for a class of scalar distributed transp... more ABSTRACT The paper considers the observer design problem for a class of scalar distributed transport-reaction systems with boundary measurements, mixed Dirichlet-Neumann boundary conditions, linear (diffusive-convective) transport and nonlinear conically bounded source. A direct Lyapunov method is developed for the exponential stability analysis of the observation error. The Lyapunov functional is chosen with a constant kernel for the small values of the so-called Peclet number (i.e. the quotient of diffusion to convection time) and with a spatial-dependent kernel for high Peclet numbers. The derived Lyapunov-based stability conditions correspond to the ones based on the frequency-domain analysis. A numerical example illustrates the efficiency of the method.

Proceedings of the 15th IFAC World Congress, 2002, 2002

2012 IEEE 51st IEEE Conference on Decision and Control (CDC), 2012

Advances in Delays and Dynamics, 2014

ABSTRACT This chapter analyzes the exponential stability of Networked Control Systems (NCSs) with... more ABSTRACT This chapter analyzes the exponential stability of Networked Control Systems (NCSs) with communication constraints, variable sampling intervals and constant delays. We focus on static output feedback controllers for linear systems. The system sensors nodes are supposed to be distributed over a network. The scheduling of sensor information towards the controller is ruled by the classical Round-Robin protocol. We develop a time-delay approach for this problem by presenting the closed-loop system as a switched system with multiple delayed samples. By constructing an appropriate Lyapunov functional, which takes into account the switched system model and the sawtooth delays induced by sampled-data control, we derive the exponential stability conditions in terms of Linear Matrix Inequalities (LMIs). Polytopic uncertainties in the system model can be easily included in the analysis. The efficiency of the method is illustrated on the classical cart-pendulum benchmark problem.

5th IFAC Symposium on Robust Control Design (2006), 2006

Stability of linear systems with uncertain bounded time-varying delays is studied under assumptio... more Stability of linear systems with uncertain bounded time-varying delays is studied under assumption that the nominal delay values are not equal to zero. An input-output approach to stability of such systems is known to be based on the bound of the L 2-norm of a certain integral operator. There exists a bound on this operator in two cases: in the case where the delay derivative is not greater than 1 and in the case without any constraints on the delay derivative. In the present note we fill the gap between the two cases by deriving an operator bound which is an increasing and continuous function of the delay derivative upper bound d ≥ 1. For d → ∞ the new bound corresponds to the second case and improves the existing bound. As a result, improved frequency-domain and time-domain stability criteria are derived for systems with the delay derivative greater than 1.

Proceedings of the 2005 IEEE International Symposium on, Mediterrean Conference on Control and Automation Intelligent Control, 2005., 2005

9th IFAC Workshop on Time Delay Systems (2010), 2010

This paper considers interval time-varying delay systems. The time-delay interval is divided into... more This paper considers interval time-varying delay systems. The time-delay interval is divided into several zones and the systems switch among the different zones. Based on Lyapunov-Krasovskii functional methods and linear matrix inequality (LMI) techniques, Exponential stability is exploited for every time-delay zone. The global stability of the switched system is guaranteed if some minimum average dwell time conditions are satisfied. Some numerical examples and comparisons with other works show that the methods greatly enlarge the value of maximum upper-bound of time-delay for the systems.

6th IFAC Symposium on Robust Control Design, 2009, 2009

7th IFAC Symposium on Robust Control Design, 2012

IEEE Transactions on Automatic Control, 2002

In this note, we combine a new approach for linear timedelay systems based on a descriptor repres... more In this note, we combine a new approach for linear timedelay systems based on a descriptor representation with a recent result on bounding of cross products of vectors. A delay-dependent criterion for determining the stability of systems with time-varying delays is obtained. This criterion is used to derive an efficient stabilizing state-feedback design method for systems with parameter uncertainty, of either the polytopic or the norm-bounded types.

IEEE Transactions on Automatic Control, 2003

A new robust delay dependent stability test is introduced that determines the asymptotic stabilit... more A new robust delay dependent stability test is introduced that determines the asymptotic stability of linear systems with state delays. The parameters of the system are not exactly given. They are known to reside in a given polytope. The test provides an efficient sufficient condition for the stability of the system over the uncertainty polytope. This condition is parameter dependent and it therefore improves previous results that were derived using a single Lyapunov-Krasovskii functional. The stability test is readily extended to provide a criterion for robust stabilization via statefeedback.

Asian Journal of Control, 2008

This paper investigates the robust stability of linear neutral systems with mixed delays and norm... more This paper investigates the robust stability of linear neutral systems with mixed delays and norm-bounded uncertainty. Using new Lyapunov-Krasovskii functionals, less conservative delay-dependent robust stability conditions for such systems in terms of linear matrix inequalities (LMIs) are derived. Numerical examples show that the results obtained in this paper significantly improve the estimate of the stability limit over some existing results in other literature.

International Journal of Control, 2009

Sampled-data H 1 control of linear systems with constant state, control and measurement delays is... more Sampled-data H 1 control of linear systems with constant state, control and measurement delays is considered. The sampling of the controlled input and of the measured output is not assumed to be uniform. The system is modelled as a continuous-time one, where the controlled input and the measurement output have piecewise-continuous delays. The input-output approach to stability and L 2-gain analysis is applied to the resulting system. The discretised Lyapunov functional method is extended to the case of multiple delays, where the Lyapunov functional is complete in one of the delays (in the state) and is simple in the other delays (those in the input and in the output), which are constant. Solutions to the state-feedback and the outputfeedback H 1 control problems are derived in terms of linear matrix inequalities (LMIs).

International Journal of Control, 2005

Robust stability and the guaranteed cost control problem are considered for discrete-time systems... more Robust stability and the guaranteed cost control problem are considered for discrete-time systems with time-varying delays from given intervals. A new construction of Lyapunov-Krasovskii functionals (LKFs), which has been recently introduced in the continuous-time case, is applied. To a nominal LKF, which is appropriate to the system with nominal delays, terms are added that correspond to the system with the perturbed delays and that vanish when the delay perturbations approach zero. The nominal LKF is chosen in the form of the descriptor type and is applied either to the original or to the augmented system. The delayindependent result is derived via the Razumikhin approach. Guaranteed cost state-feedback control is designed. The advantage of the new tests is demonstrated via illustrative examples.

IEEE Transactions on Automatic Control, 2009

It is well known that for linear, uncertain systems, a static output feedback sliding mode contro... more It is well known that for linear, uncertain systems, a static output feedback sliding mode controller can only be determined if a particular triple associated with the reduced order dynamics in the sliding mode is stabilisable. This paper shows that the static output feedback sliding mode control design problem can be solved for a broader class of systems if a known delay term is deliberately introduced into the switching function. Effectively the reduced order sliding mode dynamics are stabilized by the introduction of this artificial delay.

Abstract For linear singularly perturbed system with delay sufficient conditions for stability fo... more Abstract For linear singularly perturbed system with delay sufficient conditions for stability for all small enough values of singular perturbation parameter e are obtained in the general case, when delay and ξ are independent. The sufficient delay-dependent conditions are given in terms of linear matrix inequalities (LMIs) by applying an appropriate Lyapunov-Krasovskii functional. LMIs are derived by using a descriptor model transformation and Park's inequality for bounding cross terms. A memoryless state-feedback stabilizing controller is obtained. Numerical examples illustrate the effectiveness of the new theory.

Proceedings. 1996 IEEE International Workshop on Variable Structure Systems. - VSS'96 -, 2000

The second order relay control systems with delay (S O R C S D) are considered. It is shown that ... more The second order relay control systems with delay (S O R C S D) are considered. It is shown that the average frequency of any oscillatory solution of S O R C S D after a finite time interval becomes a constant. We give Sumcient conditions for the existence of periodic oscillations in S O R C S D for any frequency, and sumcient conditions for the orbital asymptotic stability of periodic oscillations with the minimal (zero) average frequency.

Systems & Control Letters, 2014

ABSTRACT The paper considers a distributed robust estimation problem over a network with directed... more ABSTRACT The paper considers a distributed robust estimation problem over a network with directed topology involving continuous time observers. While measurements are available to the observers continuously, the nodes interact according to a Round-Robin rule, at discrete time instances. The results of the paper are sufficient conditions which guarantee a suboptimal H∞H∞ level of consensus between observers with sampled interconnections.

6th IFAC Symposium on Robust Control Design, 2009, 2009

ABSTRACT The paper considers the observer design problem for a class of scalar distributed transp... more ABSTRACT The paper considers the observer design problem for a class of scalar distributed transport-reaction systems with boundary measurements, mixed Dirichlet-Neumann boundary conditions, linear (diffusive-convective) transport and nonlinear conically bounded source. A direct Lyapunov method is developed for the exponential stability analysis of the observation error. The Lyapunov functional is chosen with a constant kernel for the small values of the so-called Peclet number (i.e. the quotient of diffusion to convection time) and with a spatial-dependent kernel for high Peclet numbers. The derived Lyapunov-based stability conditions correspond to the ones based on the frequency-domain analysis. A numerical example illustrates the efficiency of the method.

Proceedings of the 15th IFAC World Congress, 2002, 2002

2012 IEEE 51st IEEE Conference on Decision and Control (CDC), 2012

Advances in Delays and Dynamics, 2014

ABSTRACT This chapter analyzes the exponential stability of Networked Control Systems (NCSs) with... more ABSTRACT This chapter analyzes the exponential stability of Networked Control Systems (NCSs) with communication constraints, variable sampling intervals and constant delays. We focus on static output feedback controllers for linear systems. The system sensors nodes are supposed to be distributed over a network. The scheduling of sensor information towards the controller is ruled by the classical Round-Robin protocol. We develop a time-delay approach for this problem by presenting the closed-loop system as a switched system with multiple delayed samples. By constructing an appropriate Lyapunov functional, which takes into account the switched system model and the sawtooth delays induced by sampled-data control, we derive the exponential stability conditions in terms of Linear Matrix Inequalities (LMIs). Polytopic uncertainties in the system model can be easily included in the analysis. The efficiency of the method is illustrated on the classical cart-pendulum benchmark problem.

5th IFAC Symposium on Robust Control Design (2006), 2006

Stability of linear systems with uncertain bounded time-varying delays is studied under assumptio... more Stability of linear systems with uncertain bounded time-varying delays is studied under assumption that the nominal delay values are not equal to zero. An input-output approach to stability of such systems is known to be based on the bound of the L 2-norm of a certain integral operator. There exists a bound on this operator in two cases: in the case where the delay derivative is not greater than 1 and in the case without any constraints on the delay derivative. In the present note we fill the gap between the two cases by deriving an operator bound which is an increasing and continuous function of the delay derivative upper bound d ≥ 1. For d → ∞ the new bound corresponds to the second case and improves the existing bound. As a result, improved frequency-domain and time-domain stability criteria are derived for systems with the delay derivative greater than 1.

Proceedings of the 2005 IEEE International Symposium on, Mediterrean Conference on Control and Automation Intelligent Control, 2005., 2005

9th IFAC Workshop on Time Delay Systems (2010), 2010

This paper considers interval time-varying delay systems. The time-delay interval is divided into... more This paper considers interval time-varying delay systems. The time-delay interval is divided into several zones and the systems switch among the different zones. Based on Lyapunov-Krasovskii functional methods and linear matrix inequality (LMI) techniques, Exponential stability is exploited for every time-delay zone. The global stability of the switched system is guaranteed if some minimum average dwell time conditions are satisfied. Some numerical examples and comparisons with other works show that the methods greatly enlarge the value of maximum upper-bound of time-delay for the systems.

6th IFAC Symposium on Robust Control Design, 2009, 2009

7th IFAC Symposium on Robust Control Design, 2012