Rank-one LMI approach to simultaneous stabilization of linear systems

被引：37

作者：

Henrion, D

Tarbouriech, S

Sebek, M

机构：

[1] CNRS, LAAS, F-31077 Toulouse 4, France

[2] Acad Sci Czech Republic, Inst Informat Theory & Automat, Prague 18208 8, Czech Republic

[3] Czech Tech Univ, Fac Elect Engn, Trnka Lab Automat Control, Prague 16627 6, Czech Republic

来源：

SYSTEMS & CONTROL LETTERS | 1999年 / 38卷 / 02期

关键词：

simultaneous stabilization; BMI problem; LMI problem; rank constraint; potential reduction; ellipsoid intersection;

D O I：

10.1016/S0167-6911(99)00049-3

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Following a polynomial approach to control design, the simultaneous stabilization by a controller of given fixed order of a family of SISO linear systems is interpreted as an NP-hard BMI feasibility problem. Upon formulating this BMI problem as an LMI problem with an additional non-convex rank constraint, two simultaneous stabilization methods are then proposed, The first method is a heuristic algorithm performing rank minimization by potential reduction. The second method hinges upon necessary conditions and sufficient conditions for simultaneous stabilization derived from geometric properties of the intersection of a set of ellipsoids. Both methods are then illustrated by numerical examples. (C) 1999 Elsevier Science B.V. All rights reserved.

引用

页码：79 / 89

页数：11

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[1] OUTPUT FEEDBACK STABILIZATION AND RELATED PROBLEMS - SOLUTION VIA DECISION METHODS [J].