Parameter dependent Lyapunov functions for a class of uncertain linear systems: an LMI approach

Author

Net, Alexandre Trofino

Author_Institution

Dept. of Syst. & Autom., Fed. Univ. of Santa Catarina, Florianopolis, Brazil

Volume

3

fYear

1999

fDate

1999

Firstpage

2341

Abstract

The paper deals with the robust stability of linear systems with real time varying parameters with magnitude and rate of change which are confined to a given polytope. The system is described by a set of differential and algebraic equations and the system matrices may be polynomial functions of the uncertain parameters. We present LMI conditions for the construction of Lyapunov functions that depend quadratically on the uncertain parameters. The well known quadratic stability notion, based on quadratic Lyapunov functions, is also studied, connections are established and numerical examples illustrate the main results

Keywords

Lyapunov methods; differential equations; linear systems; matrix algebra; robust control; time-varying systems; uncertain systems; LMI approach; LMI conditions; algebraic equations; differential equations; parameter dependent Lyapunov functions; polynomial functions; polytope; quadratic Lyapunov functions; quadratic stability notion; rate of change; real time varying parameters; robust stability; system matrices; uncertain linear systems; uncertain parameters; Automation; Equations; Linear systems; Lyapunov method; Polynomials; Real time systems; Robust stability; State-space methods; System testing; Uncertainty;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1999. Proceedings of the 38th IEEE Conference on

Conference_Location

Phoenix, AZ

ISSN

0191-2216

Print_ISBN

0-7803-5250-5

Type

conf

DOI

10.1109/CDC.1999.831273

Filename

831273