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

Hicham El Aiss, Taha Zoulagh, Abdelaziz Hmamed and Ahmed El Hajjaji

International Journal of Systems Science, 2019, vol. 50, issue 1, 35-49

Abstract: 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.

Date: 2019
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DOI: 10.1080/00207721.2018.1543474

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