A new approach to robust \(\mathcal H_{\infty }\) filtering for uncertain systems with both discrete and distributed delays. (English) Zbl 1118.93024

Wu, Ligang; Shi, Peng; Gao, Huijun; Wang, Changhong

Circuits Syst. Signal Process. 26, No. 2, 229-248 (2007).

Summary: This paper is concerned with robust \(H_{\infty }\) filter design for a class of linear distributed delay systems with norm-bounded time-varying parameter uncertainties. The distributed delays are assumed to appear in both state and measurement equations. A new design method is proposed by introducing some relaxation matrices and tuning parameters, which can be chosen properly to lead to a less conservative result. A sufficient condition is obtained to guarantee the existence of desired \(H_{\infty }\) filters, which can be constructed by solving a convex optimization problem. A numerical example is included to illustrate the effectiveness and the reduced conservatism of the proposed design technique.

MSC:

93B36	\(H^\infty\)-control
93C41	Control/observation systems with incomplete information
93C15	Control/observation systems governed by ordinary differential equations
93C05	Linear systems in control theory
93D09	Robust stability

Keywords:

distributed delay; \({\mathcal H}_\infty\) filtering; robust filtering; uncertain systems; linear matrix inequalities; LMI