Exponential L2L? L 2  L ? filtering for distributed delay systems with Markovian jumping parameters ?
This paper is concerned with the problem of exponential L2L? L 2  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 L2L? L 2  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 LyapunovKrasovskii 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 delays decay-rate-dependent conditions exponential stability l2l? l 2  l ? filtering l2l? l 2  l ? l2l? l 2  l ? l 2  l ? markovian jump systems