Robust H∞ deconvolution filter for polytopic uncertain systems with distributed delay

This paper is concerned with the robust H∞ deconvolution filtering problem for polytopic uncertain systems with distributed delay. The objective is to design a full-order deconvolution filter such that the filtering error system is not only asymptotically stable, but also satisfies a prescribed H∞ performance level for all uncertainties. Based on employing the parameter-dependent Lyapunov–Krasovskii functional method, a sufficient condition is proposed for solvability of this problem in terms of linear matrix inequalities. In order to reduce the conservatism, two approaches, namely, the integral partitioning approach, and the homogeneous polynomial parameter-dependent matrix approach, are applied. Finally, two numerical simulations are provided to demonstrate the effectiveness of the proposed methods in this paper.