Stability analysis for switched systems with continuous-time and discrete-time subsystems

• Published in: 2004 American Control Conference Proceedings; Volume 5 of 6 Vol. 5; pp. 4555 - 4560 vol.5
• Main Authors: Zhai, G., Hai Lin, Michel, A.N., Yasuda, K.
• Format: Conference Proceeding Journal Article
• Language: English
• Published: Piscataway NJ IEEE 01.01.2004; Evanston IL American Automatic Control Council
• Subjects: Adaptive control; Applied sciences; Computer science; control theory; systems; Control systems; Control theory. Systems; Environmental factors; Exact sciences and technology; Lyapunov method; Mechanical engineering; Stability analysis; Sufficient conditions; Switched systems; Symmetric matrices; Multimodel control; Hurwitz polynomial; Linear time invariant system; Time average; Discrete time; Continuous time; Exponential stability; Switching; Lyapunov function; Hybrid system
• ISBN: 9780780383357; 0780383354
• ISSN: 0743-1619
• DOI: 10.23919/ACC.2004.1384029

We study stability property for a new type of switched systems which are composed of a continuous-time LTI subsystem and a discrete-time LTI subsystem. When the two subsystems are Hurwitz and Schur stable, respectively, we show that if the subsystem matrices commute each other, or if they are symmetric, then a common Lyapunov function exists for the two subsystems and that the switched system is exponentially stable under arbitrary switching. Without the assumption of commutation or symmetricity condition, we show that the switched system is exponentially stable if the average dwell time between the subsystems is larger than a specified constant. When neither of the two subsystems is stable, we propose a sufficient condition in the form of a combination of the two subsystem matrices, under which we propose a stabilizing switching law.