Stability and stabilization of piecewise affine and hybrid systems: an LMI approach

Author

Mignone, Domenico ; Ferrari-Trecate, Giancarlo ; Morari, Manfred

Author_Institution

Inst. fur Autom., Eidgenossische Tech. Hochschule, Zurich, Switzerland

Volume

1

fYear

2000

fDate

2000

Firstpage

504

Abstract

In this paper we present various algorithms both for stability analysis and state-feedback design for discrete-time piecewise affine systems. Our approach hinges on the use of piecewise quadratic Lyapunov functions that can be computed as the solution of a set of linear matrix inequalities. We show that the continuity of the Lyapunov function is not required in the discrete-time case. Moreover, the basic algorithms are made less conservative by exploiting the switching structure of piecewise affine systems and by using relaxation procedures

Keywords

Lyapunov matrix equations; control system analysis; control system synthesis; discrete time systems; matrix algebra; piecewise polynomial techniques; stability; state feedback; LMI; LMI approach; Lyapunov function; discrete-time piecewise affine systems; hybrid systems; linear matrix inequalities; piecewise quadratic Lyapunov functions; relaxation procedures; stability analysis; stabilization; state-feedback design; Algorithm design and analysis; Automata; Linear matrix inequalities; Logic; Lyapunov method; Predictive models; Robust stability; Stability analysis; Sufficient conditions; System testing;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2000. Proceedings of the 39th IEEE Conference on

Conference_Location

Sydney, NSW

ISSN

0191-2216

Print_ISBN

0-7803-6638-7

Type

conf

DOI

10.1109/CDC.2000.912814

Filename

912814