A New Approach to $H_{\infty }$ Filter Design for Systems With Time-Varying State Delay

This brief revisits the robust H_∞ filter design problem for systems with a time-varying state delay by an indirect approach. By employing a two-term approximation method, the filtering error system with a time-varying delay is reformulated into a feedback interconnection form, which contains a forward system with two constant time delays and a feedback system with uncertainties. Then, based on the scaled small gain theorem, the asymptotic stability of the filtering error system is examined, and a new delay-dependent bounded real lemma (BRL) is obtained. Based on the BRL, both the full- and reduced-order filter design approaches are proposed. Moreover, immediate extensions of the results are made to systems with polytopic uncertainties. Finally, two illustrative examples are presented to demonstrate the validity of the proposed methods.