zbMATH — the first resource for mathematics

Non-fragile decentralized $$H_{\infty }$$ controller design for uncertain linear systems. (English) Zbl 1232.93008
Summary: Considering the design problem of non-fragile decentralized $$H_{\infty }$$ controller with gain variations, the dynamic feedback controller by measurement feedback for uncertain linear systems is constructed and studied. The parameter uncertainties are considered to be unknown but norm bounded. The design procedures are investigated in terms of positive definite solutions to modify algebraic Riccati inequalities. Using information exchange among local controllers, the designed non-fragile decentralized $$H_{\infty }$$ controllers guarantee that the uncertain closed-loop linear systems are stable and with $$H_{\infty }$$ -norm bound on disturbance attenuation. A sufficient condition that there are such non-fragile $$H_{\infty }$$ controllers is obtained by algebraic Riccati inequalities. The approaches to solve modified algebraic Riccati inequalities are carried out preliminarily. Finally, a numerical example to show the validity of the proposed approach is given.

MSC:
 93A14 Decentralized systems 93B36 $$H^\infty$$-control 93B52 Feedback control 93C05 Linear systems in control theory
Full Text: