An Extension of Lie Algebraic Stability Analysis for Switched Systems with Continuous-Time and Discrete-Time Subsystems

Author

Zhai, Guisheng ; Xu, Xuping ; Lin, Hai ; Liu, Derong

Author_Institution

Dept. of Mech. Eng., Osaka Prefecture Univ., Sakai

fYear

0

fDate

0-0 0

Firstpage

362

Lastpage

367

Abstract

We 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

Keywords

Lie algebras; Lyapunov methods; asymptotic stability; continuous time systems; discrete time systems; matrix algebra; time-varying systems; Hurwitz-Schur stability; Lie algebraic stability analysis; arbitrary switching; continuous-time subsystem; discrete-time subsystem; dwell time scheme; exponential stability; quadratic Lyapunov function; subsystem matrices; switched systems; Algebra; Books; Computer science education; Control systems; Linear systems; Lyapunov method; Mechanical engineering; Regulators; Stability analysis; Switched systems; Lie algebra; Switched systems; arbitrary switching; common quadratic Lyapunov (Lyapunov-like) functions; dwell time scheme; exponential stability;

fLanguage

English

Publisher

ieee

Conference_Titel

Networking, Sensing and Control, 2006. ICNSC '06. Proceedings of the 2006 IEEE International Conference on

Conference_Location

Ft. Lauderdale, FL

Print_ISBN

1-4244-0065-1

Type

conf

DOI

10.1109/ICNSC.2006.1673173

Filename

1673173