Deconvolution filtering for stochastic systems via homogeneous polynomial Lyapunov functions

This paper deals with the robust H∞H∞ and L2–L∞L2–L∞ deconvolution filtering problems for stochastic systems with polytopic uncertainties. The purpose is to design a full-order deconvolution filter such that (i) the deconvolution error system is robustly exponentially mean-square stable with a prescribed decay rate and (ii) an H∞H∞ or L2–L∞L2–L∞ performance of the deconvolution error system is guaranteed. Based on a homogeneous polynomial parameter-dependent matrix (HPPDM) approach, sufficient conditions for the solvability of these problems are given in terms of linear matrix inequalities (LMIs). Such conditions are dependent on the decay rate, which enables one to design robust deconvolution filters by selecting the decay rates according to different practical conditions. In addition, when these LMIs are feasible, a design procedure of the desired filters is developed and an exponential estimate for the deconvolution error system is given. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed design methods.