A note on quadratic stability of uncertain linear discrete-time systems

Author

Amato, Francesco ; Mattei, Massimiliano ; Pironti, Alfredo

Author_Institution

Dipt. di Inf. e Sistemistica, Naples Univ., Italy

Volume

43

Issue

2

fYear

1998

fDate

2/1/1998 12:00:00 AM

Firstpage

227

Lastpage

229

Abstract

In this paper we consider a linear discrete-time system depending on a vector of uncertain parameters. Assuming that the system matrix depends on parameters as the ratio of a multiaffine matrix-valued function and a multiaffine polynomial and that the parameters range in a hyper-rectangle, we show that the uncertain system is quadratically stable if and and only if the set of vertex systems is quadratically stable. This allows us to state a necessary and sufficient condition for quadratic stability in terms of the solvability of a feasibility problem involving linear matrix inequalities

Keywords

control system analysis; discrete time systems; linear systems; matrix algebra; stability; uncertain systems; discrete-time systems; linear matrix inequality; linear systems; multiaffine matrix-valued function; multiaffine polynomial; necessary condition; quadratic stability; sufficient condition; uncertain systems; Linear matrix inequalities; Linear systems; Performance evaluation; Polynomials; Stability; Sufficient conditions; Testing; Time varying systems; Uncertain systems; Vectors;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.661070

Filename

661070