The Bounded Real Lemma for Internally Positive Systems and H-Infinity Structured Static State Feedback

Author

Tanaka, Takashi ; Langbort, Cédric

Author_Institution

Dept. of Aerosp. Eng., Univ. of Illinois at Urbana-Champaign, Urbana, IL, USA

Volume

56

Issue

9

fYear

2011

Firstpage

2218

Lastpage

2223

Abstract

We consider the bounded real lemma for internally positive linear time-invariant systems. We show that the H_∞ norm of such systems can be evaluated by checking the existence of a certain diagonal quadratic storage function. Taking advantage of this fact, the problem of designing a structured static state feedback controller achieving internal stability, contractiveness, and internal positivity in closed loop becomes convex and tractable.

Keywords

H^∞ control; closed loop systems; convex programming; decentralised control; linear matrix inequalities; stability; state feedback; H∞ norm; H-infinity structured static state feedback; bounded real lemma; closed loop; contractiveness; decentralized control; diagonal quadratic storage function; internal positivity; internal stability; internally positive linear time-invariant systems; internally positive systems; linear matrix inequality; structured static state feedback controller; Computed tomography; Control design; Linear matrix inequalities; Stability analysis; State feedback; Symmetric matrices; Decentralized control; linear matrix inequality (LMI); positive systems;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2011.2157394

Filename

5772915