A path-following method for solving BMI problems in control

Author

Hassibi, Arash ; How, Jonathan ; Boyd, Stephen

Author_Institution

Inf. Syst. Lab., Stanford Univ., CA, USA

Volume

2

fYear

1999

fDate

2-4 Jun 1999

Firstpage

1385

Abstract

We present a path-following (homotopy) method for (locally) solving bilinear matrix inequality (BMI) problems in control. The method is to linearize the BMI using a first order perturbation approximation, and then iteratively compute a perturbation that “slightly” improves the controller performance by solving a semidefinite program. This process is repeated until the desired performance is achieved, or the performance cannot be improved any further. While this is an approximate method for solving BMIs, we present several examples that illustrate the effectiveness of the approach

Keywords

closed loop systems; feedback; linear systems; mathematical programming; matrix algebra; robust control; bilinear matrix inequality; closed loop systems; feedback; iterative method; linear time invariant systems; low authority control; path-following; perturbation approximation; robust control; semidefinite programming; Control systems; Damping; Force control; Information systems; Laboratories; Linear matrix inequalities; Linear programming; Los Angeles Council; Nonlinear control systems; Open loop systems;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference, 1999. Proceedings of the 1999

Conference_Location

San Diego, CA

ISSN

0743-1619

Print_ISBN

0-7803-4990-3

Type

conf

DOI

10.1109/ACC.1999.783595

Filename

783595