Maximizing the stability radius: an LMI approach

Author

Oari, C. ; Stefan, R. ; Van Dooren, P.

Author_Institution

Dept. of Autom. Control, Univ. Polytechnica Bucharest, Romania

Volume

4

fYear

2001

fDate

2001

Firstpage

3035

Abstract

Given a stabilizable linear system Ex˙ = Ax + Bu with sE - A regular, we analyze the stability robustness of the closed-loop system (E + BK) = (A + BF)x + v, obtained by proportional and derivative (PD) state feedback u = Fx Kx˙ + v. Our goal is to maximize the stability radius of the closed-loop system matrix s(E + BK) - (A + BF) over all stabilizing PD state feedback control laws. This problem turns out to be equivalent to a particular H^∞control problem for a generalized state-space system and reduces to a system of matrix inequalities. Under certain conditions the problem actually reduces to an LMI system. We also show how to apply these ideas to higher order dynamical systems

Keywords

H^∞ control; closed loop systems; continuous time systems; eigenvalues and eigenfunctions; linear systems; matrix algebra; robust control; state feedback; state-space methods; two-term control; H^∞control problem; LMI approach; PD state feedback; closed-loop system; generalized state-space system; linear matrix inequalities; stability radius; stability robustness; stabilizable linear system; Automatic control; Control systems; Eigenvalues and eigenfunctions; Linear matrix inequalities; Linear systems; PD control; Proportional control; Robust stability; Stability analysis; State feedback;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference, 2001. Proceedings of the 2001

Conference_Location

Arlington, VA

ISSN

0743-1619

Print_ISBN

0-7803-6495-3

Type

conf

DOI

10.1109/ACC.2001.946380

Filename

946380