An input–output approach to reduced filter design for polytopic time-varying delay systems

This paper discusses the problem of delay-dependent robust $ H_{\infty } $ H∞ filtering design for polytopic systems with a time-varying delay. A new model transformation is firstly applied by employing a three-term approximation for the delayed state, which leads to a smaller approximation error than the two-term approximation. Then, based on the scaled small-gain Theorem combined with an appropriate Lyapunov–Krasovskii Functional, the $ H_{\infty } $ H∞ performance analysis of the filtering error system is examined and then the $ H_{\infty } $ H∞ full- and reduced-order filters are designed in terms of linear matrix inequalities via a simple linearisation technique. Before the end, a sufficient condition is presented to solve the problem of $ H_{\infty } $ H∞ filtering design for a time-delay system without polytopic uncertainties. Finally, illustrative examples are presented to demonstrate the validity of the proposed methods.