New results on robust energy-to-peak filtering for discrete-time switched polytopic linear systems with time-varying delay

The problem of delay-dependent robust energy-to-peak filtering design for a class of discrete-time switched linear systems with a time-varying state delay and polytopic uncertainties is revisited. The objective is to design a homogeneous switched linear filter guaranteeing the exponential stability of the resulting filtering error system with a minimised robust energy-to-peak disturbance attenuation level under average dwell-time switching scheme. Based on a novel delay and parameter-dependent discontinuous switched Lyapunov–Krasovskii functional combined with Finsler's lemma, a new sufficient condition for robust exponential stability and energy-to-peak performance analysis is first 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.