A qualitative bound in robustness of stabilization by state feedback

Author

Olbrot, Andrzej W. ; Cieslik, Joanna

Author_Institution

Dept. of Electr. Eng., Minnesota Univ., Minneapolis, MN, USA

Volume

33

Issue

12

fYear

1988

Firstpage

1165

Lastpage

1166

Abstract

It is proved that placing the poles of a linear time-invariant system arbitrarily far to the left of the imaginary axis is not possible if small perturbations in the model coefficients are taken into account. Given a nominal controllable system (A/sub 0/, B/sub 0/) with one input and at least two states and an open ball around B/sub 0/ (no matter how small), there exists a real number gamma and a perturbation B within that ball such that for any feedback matrix K placing the eigenvalues of A/sub 0/+B/sub 0/K to the left of Res= gamma , there is an eigenvalue of A/sub 0/+BK with real part not less than gamma .<>

Keywords

control system analysis; feedback; linear systems; poles and zeros; stability; eigenvalues; linear time-invariant system; model coefficients; nominal controllable system; perturbations; poles; qualitative bound; robustness; stability; stabilization; state feedback; Control systems; Control theory; Eigenvalues and eigenfunctions; Equations; Linear feedback control systems; Polynomials; Robustness; Sensitivity analysis; State feedback; Uncertainty;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.14441

Filename

14441