Min-switching local stabilization for discrete-time switching systems with nonlinear modes (original) (raw)
Related papers
A new class of Lyapunov functions for nonstandard switching systems: The stability analysis problem
IEEE Conference on Decision and Control and European Control Conference, 2011
This paper presents a new class of Lur'e type Lyapunov functions for a discrete-time switched system interconnected with a switched nonlinearity satisfying a modedependent cone bounded condition. This function includes the mode-dependent nonlinearity, but not its integral. Such a Lyapunov function allows to obtain sufficient conditions in terms of linear matrix inequalities (LMI), for the stability analysis in two different frameworks: global stability analysis for the considered systems and local stability analysis for these systems with an additional saturating input consisting of a switched linear state feedback. In the second case, an optimization problem based on these sufficient conditions is provided to enlarge the estimation of the basin of attraction, which may be composed of non-convex and disconnected sets, because of the presence of the nonlinearities in the Lyapunov function. Some numerical examples are presented to highlight the relevance of the new Lyapunov function and of the proposed method.
Stability analysis of discrete-time LPV switched systems
IFAC-PapersOnLine, 2020
This paper addresses the stability problem for discrete-time switched systems under autonomous switching. Each mode of the switched system is modeled as a Linear Parameter Varying (LPV) system, the time-varying parameters can vary arbitrarily fast and are represented in a polytopic form. The Lyapunov theory is employed to get new conditions in the form of parameter-dependent LMIs. The constructed Lyapunov function takes advantage of using an augmented state vector with shifted states in its construction. In this sense, the Lyapunov function employed in this paper can be viewed as a discrete-time LPV switched Lyapunov function. Numerical experiments illustrate the efficacy of the technique in providing stability certificates.
2012 American Control Conference (ACC), 2012
This paper addresses the switching control synthesis problem of discrete-time switched linear systems. A particular class of matrix inequalities, the so-called Lyapunov-Metzler inequalities is modified to provide conditions for stability analysis and output feedback control synthesis under a relaxed min-switching logic. The switching rule combined with switching output feedback controllers are designed to stabilize the switched closed-loop system and satisfy a pre-specified ℓ2 gain performance. The proposed switching control approach is to reduce the high frequency switches commonly observed in min-switching strategy based designs. The effectiveness of the proposed approach is illustrated through a numerical example.
Mode-Independent State Feedback Design For Discrete Switched Linear Systems
This paper addresses the stabilization problem of discrete switched linear systems. When the mode is available, a mode-dependent state feedback controller is developed. The main contribution of this note is to provide a less conservative approach to design the mode-independent state feedback controller where the switching mode is not accessible. Both design procedures are expressed in terms of linear matrix inequalities (LMIs). In fact, the new approach provides a family of LMI parameterized by a scalar variable which makes it useful for designing a mode-independent controller and offering an additional degree of freedom. Numerical evaluation is provided to show the effectiveness of the proposed conditions.
2014
This paper addresses the estimation of the domain of attraction for discrete-time nonlinear systems where the vector field is subject to changes. Firstly, the paper considers the case of switched systems, where the vector field is allowed to arbitrarily switch among the elements of a finite family. Secondly, the paper considers the case of hybrid systems, where the state space is partitioned into several regions described by polynomial inequalities, and the vector field is defined on each region independently from the other ones. In both cases, the problem consists of computing the largest sublevel set of a Lyapunov function included in the domain of attraction. An approach is proposed for solving this problem based on convex programming, which provides a guaranteed inner estimate of the sought sublevel set. The conservatism of the provided estimate can be decreased by increasing the size of the optimization problem. Some numerical examples illustrate the proposed approach.
IFAC-PapersOnLine, 2020
This paper addresses Lyapunov characterizations of input-to-state stability for nonlinear switched discrete-time systems via finite-step Lyapunov functions with respect to closed sets. The use of finite-step Lyapunov functions permits not-necessarily input-to-state stable systems in the systems family, while input-to-state stability of the resulting switched system is ensured. The result is generally presented for systems under arbitrary switching. It additionally covers the case of constrained switchings. We illustrate the effectiveness of our results by application to networked control systems with periodic scheduling policies under a priori known and dwell time-based switching mechanism.
Discrete-Time Switched Systems: Pole Location and Structural Constrained Control
This paper addresses the problem of state feedback control of discrete-time switched systems with linear modes of operation. Sufficient linear matrix inequality conditions are given for the existence of a state feedback control law assuring: i) pole location inside a circle for each linear mode of operation; iiJ overall stability for any arbitrarily fast switching sequence. Two feedback control laws are investigated: the first one with a fixed gain for all linear modes and the second using a switched gain. Moreover, structural constraints such as decentra1,ization can be easily imposed to the feedback gains. Simulation results show that with the switched gain more stringent design specifications can he imposed to the closed-loop system, providing closed-loop performances that cannot be produced by means of a constant feedback gain.
IEEE Transactions on Automatic Control, 2017
In this note, the globally exponential stability of discrete-time switched systems under arbitrary switching is investigated. First, for discrete-time switched nonlinear systems, the globally exponential stability is found to be equivalent to the existence of an M-step sequence with sufficient length and a family of Lyapunov functions, and then a stability criterion is proposed for the nominal linear case in the framework of quadratic Lyapunov function. In order to extend the stability criterion to handle uncertainties, an equivalent condition which has a promising feature that is convex in system matrices is derived, leading to a robust stability criterion for uncertain discrete-time switched linear systems. Moreover, also taking advantage of the convex feature, the disturbance attenuation performance in the sense of 2-gain is studied. Several numerical examples are provided to illustrate our approach.
Stabilization of Uncertain State Constrained Discrete-Time Switched Systems
Proceedings of the 18th IFAC World Congress, 2011
This paper presents sufficient conditions for the stabilization of constrained switched discretetime linear systems with polytopic uncertainties. A strategy of conception of switched laws from the solution of Lyapunov-Metzler inequalities is developed. Two numerical examples are used to illustrate the proposed technique.
Analysis and control of switched linear systems via modified Lyapunov-Metzler inequalities
International Journal of Robust and Nonlinear Control, 2014
This paper addresses analysis and switching control problems of continuous/discrete-time switched linear systems. A particular class of matrix inequalities, the so-called Lyapunov-Metzler inequalities, will be modified to provide conditions for stability analysis and output feedback control synthesis under a relaxed min-switching logic. The switching rule combined with switching output feedback controllers will be designed to stabilize the switched system and satisfy a prespecified L 2 (`2) gain performance. The proposed analysis and switching control approach could refrain frequent switches commonly observed in minswitching based designs. The effectiveness of the proposed approach will be illustrated through numerical examples.