Stability analysis for a class of nonlinear switched systems (original) (raw)
Related papers
A general stability criterion for switched linear systems having stable and unstable subsystems
International Journal of Adaptive Control and Signal Processing, 2012
SUMMARYWe report conditions on a switching signal that guarantee that solutions of a switched linear system converge asymptotically to zero. These conditions apply to continuous, discrete‐time and hybrid switched linear systems, those having both stable subsystems and mixtures of stable and unstable subsystems. Copyright © 2012 John Wiley & Sons, Ltd.
Stability of a Switched Linear System
2012
Hybrid systems are dynamic systems that arise out of the interaction of continuous state dynamics and discrete state dynamics. Switched systems, which are a type of hybrid system, have been given much attention by control systems research over the past decade. Problems with the controllability, observability, converseability and stabilizability of switched systems have always been discussed. In this paper, the trend in research regarding the stability of switched systems will be investigated. Then the variety of methods that have been discovered by researchers for stabilizing switched linear systems with arbitrary switching will be discussed in detail.
International Journal of Applied Mathematics and Computer Science, 2007
Extended Lie Algebraic Stability Analysis for Switched Systems with Continuous-Time and Discrete-Time SubsystemsWe analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by all subsystem matrices, we show that if all subsystems are Hurwitz/Schur stable and this Lie algebra is solvable, then there is a common quadratic Lyapunov function for all subsystems and thus the switched system is exponentially stable under arbitrary switching. When not all subsystems are stable and the same Lie algebra is solvable, we show that there is a common quadratic Lyapunov-like function for all subsystems and the switched system is exponentially stable under a dwell time scheme. Two numerical examples are provided to demonstrate the result.