Improved robust energy-to-peak filtering design for discrete-time switched polytopic linear systems with time-varying delay

This paper revisits the problem of delay-dependent robust energy-to-peak filtering for a class of discrete-time switched linear systems with time-varying state delay and polytopic uncertainties. The objective is to design a homogeneous switched linear filter guaranteeing the asymptotic stability of the resulting filtering error system with a minimized robust energy-to-peak disturbance attenuation level β_min. Based on a new delay and parameter-dependent switched Lyapunov-Krasovskii functional combined with Finsler's Lemma, a novel sufficient condition for robust energy-to-peak performance analysis is firstly derived and then the corresponding filter synthesis is developed. It is shown that the filter parameters can be obtained by solving a set of linear matrix inequalities. Finally, a numerical example is provided to illustrate the advantages and less conservatism of the proposed approach in comparison with the existing approaches.