scholarly journals Stability analysis of discrete-time switched systems under arbitrary switching

2018 ◽  
Vol 51 (25) ◽  
pp. 371-376 ◽  
Author(s):  
Thales S. Gomide ◽  
Márcio J. Lacerda
Keyword(s):  
Stability Analysis ◽  
Discrete Time ◽  
Switched Systems ◽  
Arbitrary Switching

scholarly journals Extended Lie Algebraic Stability Analysis for Switched Systems with Continuous-Time and Discrete-Time Subsystems

2007 ◽  
Vol 17 (4) ◽  
pp. 447-454 ◽  
Author(s):  
Guisheng Zhai ◽  
Xuping Xu ◽  
Hai Lin ◽  
Derong Liu
Keyword(s):  
Stability Analysis ◽  
Lie Algebra ◽  
Discrete Time ◽  
Continuous Time ◽  
Switched Systems ◽  
Switched System ◽  
Quadratic Lyapunov Function ◽  
Algebraic Stability ◽  
Arbitrary Switching ◽  
Exponentially Stable

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.

Stability and controllability of switched systems

2013 ◽  
Vol 61 (3) ◽  
pp. 547-555 ◽  
Author(s):  
J. Klamka ◽  
A. Czornik ◽  
M. Niezabitowski
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Linear Systems ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Switched Linear Systems ◽  
Arbitrary Switching ◽  
Mathematical Problems ◽  
The Stability ◽  
Necessary And Sufficient

Abstract The study of properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems. This paper aims to briefly survey recent results on stability and controllability of switched linear systems. 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 that, we review the controllability results.

Sign in / Sign up

Export Citation Format

Share Document