Stability of cones of polynomials. An application to the design of high-gain controllers for saturated systems

Author

Aguirre, Brandon ; Ibarra, C. ; Suárez, R.

Author_Institution

Dept. de Matematicas, Univ. Autonoma Metropolitana-Iztapalapa, Mexico

Volume

2

fYear

2000

fDate

2000

Firstpage

1087

Abstract

Hinrichsen and Kharitonov (Math. Control Signal Systems, vol.8, p.97-117, (1995) gave necessary and sufficient conditions for a convex conic set of polynomials to be Hurwitz. However, that result is not simple to apply. In this paper, an easy-to-check sufficient condition is introduced. The obtained condition is a matrix inequality which is a simple algebraic test for the stability of rays of polynomials. As an application, for stable open-loop systems, a cone of gains c such that the function u=-kc^Tx is a stabilizing control feedback for all k>0, is shown to exist. Moreover, for the same cone of gains, it was established that there do not exist any first harmonic periodic orbits despite saturation

Keywords

control system synthesis; feedback; matrix algebra; polynomials; stability; Hurwitz polynomials; convex conic polynomial set; first harmonic periodic orbits; high-gain controller design; matrix inequality; necessary and sufficient conditions; open-loop systems; polynomial cone stability; polynomial rays; saturated systems; saturation; stabilizing control feedback; Control systems; Eigenvalues and eigenfunctions; Feedback; Linear matrix inequalities; Open loop systems; Orbits; Polynomials; Stability; Sufficient conditions; 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.2000.911996

Filename

911996