Stability of switched linear discrete-time descriptor systems: a new commutation condition

• Published in: International journal of control Vol. 85; no. 11; pp. 1779 - 1788
• Main Authors: Zhai, Guisheng, Xu, Xuping, Ho, Daniel W.C.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis Group 01.11.2012; Taylor & Francis; Taylor & Francis Ltd
• Subjects: Applied sciences; common quadratic Lyapunov functions; Commutation; Computer science; control theory; systems; Control system analysis; Control theory. Systems; Exact sciences and technology; impulse-free switching; Impulses; Lyapunov functions; matrix inequalities; pairwise commutation; Stability; Studies; switched linear discrete-time descriptor systems; Switching; System theory; Multimodel control; Continuous time; matrix inequalities; Matrix inequality; switched linear discrete-time descriptor systems; Hybrid system; common quadratic Lyapunov functions; impulse-free switching; Discrete time; pairwise commutation; Linear stability; stability; Lyapunov function; Quadratic function
• ISSN: 0020-7179; 1366-5820
• DOI: 10.1080/00207179.2012.703788

In this article, we study stability of switched linear discrete-time descriptor systems. Under the assumption that all subsystems are stable and there is no impulse occurring at the switching instants, we establish a new pairwise commutation condition under which the switched system is stable. It turns out that the condition is a natural and important extension to the existing commutation conditions, and it can be applied in discretised continuous-time switched systems in a straightforward manner. Finally, we also show that when the proposed commutation condition holds, there exists a common quadratic Lyapunov function for the subsystems.