On stabilization of switched nonlinear systems with unstable modes (original) (raw)

On the -stabilization of switched nonlinear systems via state-dependent switching rule

Applied Mathematics and Computation, 2010

This paper considers switching stabilization of some general nonlinear systems. Assuming certain properties of a convex linear combination of the nonlinear vector fields, two ways of generating stabilizing switching signals are proposed, i.e., the minimal rule and the generalized rule, both based on a partition of the time-state space. The main theorems show that the resulting switched system is globally uniformly asymptotically stable and globally uniformly exponentially stable, respectively. It is shown that the stabilizing switching signals do not exhibit chattering, i.e., two consecutive switching times are separated by a positive amount of time. In addition, under the generalized rule, the switching signal does not exhibit Zeno behavior (accumulation of switching times in a finite time). Stability analysis is performed in terms of two measures so that the results can unify many different stability criteria, such as Lyapunov stability, partial stability, orbital stability, and stability of an invariant set. Applications of the main results are shown by several examples, and numerical simulations are performed to both illustrate and verify the stability analysis.

1st pages of the book : Stabilization of Switched Nonlinear Systems with Unstable Modes

2014

The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein.

On Input-To-Output Stability of Switched Nonlinear Systems

Proceedings of the 17th IFAC World Congress, 2008, 2008

The problem of input-to-output stability for switched nonlinear systems is considered.We investigate methods based both, on constant and average dwell-times. In particular, we show that constant dwell-time should depend on initial conditions and disturbances amplitudes to ensure global stability properties for a generic nonlinear switched system. IFAC Copyright 2008.

Stability analysis for a class of nonlinear switched systems

Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304), 2000

In the present paper, we study several qualitative properties of a class of nonlinear switched systems under certain switching laws. First, we show that if all the subsystems are linear time-invariant and the system matrices are commutative componentwise and stable, then the entire switched system is globally exponentially stable under arbitrary switching laws. Next, we study the above linear switched systems with certain nonlinear perturbations, which can be either vanishing or non-vanishing. Under reasonable assumptions, global exponential stability is established for these systems. We further study the stability and instability properties, under certain switching laws, for switched systems with commutative subsystem matrices that may be unstable. Results for both continuous-time and discrete-time cases are presented.

Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results

IEEE Transactions on Automatic Control, 2009

During the past several years, there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems. This paper aims to briefly survey recent results in this field. First, the stability analysis for switched systems is reviewed. We focus on the stability analysis for switched linear systems under arbitrary switching, and we highlight necessary and sufficient conditions for asymptotic stability. After a brief review of the stability analysis under restricted switching and the multiple Lyapunov function theory, the switching stabilization problem is studied, and a variety of switching stabilization methods found in the literature are outlined. Then the switching stabilizability problem is investigated, that is under what condition it is possible to stabilize a switched system by properly designing switching control laws. Note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature. A necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here.

Stability and Stabilizability of Switched Linear Systems: A Short Survey of Recent Results

2005

Integral-Input-to-State Stability of Switched Nonlinear Systems under Slow Switching

IEEE Transactions on Automatic Control

In this paper we study integral-input-to-state stability (iISS) of nonlinear switched systems with jumps. We demonstrate by examples that iISS is not always preserved under slow enough dwell time switching, and then we present sufficient conditions for iISS to be preserved under slow switching. These conditions involve, besides a sufficiently large dwell time, some additional properties of comparison functions characterizing iISS of the individual modes. When the sufficient conditions that guarantee iISS are only partially satisfied, we are then able to conclude weaker variants of iISS, also introduced in this work. As an illustration, we show that switched systems with bilinear zero-input-stable modes are always iISS under sufficiently large dwell time.

Absolute exponential stability and stabilization of switched nonlinear systems

Systems & Control Letters, 2014

This paper is concerned with the problems of absolute exponential stability and stabilization for a class of switched nonlinear systems whose system matrices are Metzler. Nonlinearity of the systems is constrained in a sector field, which is bounded by two odd symmetric piecewise linear functions. Multiple Lyapunov functions are introduced to deal with the stability of such nonlinear systems. Compared with some existing results obtained by the common Lyapunov function approach in the literature, the conservatism of our results is reduced. All present conditions can be solved by linear programming. Furthermore, the absolute exponential stabilization for the considered systems is designed by the statefeedback and average dwell time switching strategy. Two examples are also given to illustrate the validity of the theoretical findings.

On stabilization of switched nonlinear systems with unstable modes (original) (raw)

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