Exponential L2–L∞L2–L∞ filtering for distributed delay systems with Markovian jumping parameters

This paper is concerned with the problem of exponential L2–L∞L2–L∞ filter design for linear systems simultaneously with distributed delays, Markovian jumping parameters and norm-bounded parametric uncertainties. The purpose is to design full-order mode-dependent filters such that the filtering error system is not only mean-square robustly exponentially stable with a specified decay rate but also satisfies an L2–L∞L2–L∞ performance requirement. First, sufficient conditions for the stability and performance analysis of the filtering error system are derived based on a novel version of mode-dependent Lyapunov–Krasovskii functional. Then, delay-dependent and decay-rate-dependent conditions for the existence of desired filters are obtained in terms of linear matrix inequalities (LMIs). The filter coefficients can be computed by using feasible solutions of the presented LMIs. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed design method.

► Distributed delay systems with Markvoian jump parameters are considered.
► Exponential L2–L∞L2–L∞ filtering for the considered systems is investigated.
► Decay-rate-dependent conditions are presented in terms of LMIs.
► The integral-partitioning approach is used to derive the main results.