Parameterized LMIs in control theory

被引：175

作者：

Apkarian, P

Tuan, HD

机构：

[1] ONERA CERT, Control Syst Dept, F-31055 Toulouse, France

[2] Toyota Technol Inst, Dept Control & Informat, Tempa Ku, Nagoya, Aichi 4688511, Japan

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2000年 / 38卷 / 04期

关键词：

linear matrix inequalities; robust semidefinite programming; directional convexity; robustness analysis; parametric uncertainty; linear parameter-varying control;

D O I：

10.1137/S036301299732612X

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

A wide variety of problems in control system theory fall within the class of parameterized linear matrix inequalities (LMIs), that is, LMIs whose coefficients are functions of a parameter confined to a compact set. Such problems, though convex, involve an infinite set of LMI constraints and hence are inherently di cult to solve numerically. This paper investigates relaxations of parameterized LMI problems into standard LMI problems using techniques relying on directional convexity concepts. An in-depth discussion of the impact of the proposed techniques in quadratic programming, Lyapunov-based stability and performance analysis, mu analysis, and linear parameter-varying control is provided. Illustrative examples are given to demonstrate the usefulness and practicality of the approach.

引用

页码：1241 / 1264

页数：24

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