New approach to H∞ filtering for discrete-time systems with polytopic uncertainties

This paper is concerned with the problem of H∞ filtering for polytopic uncertain discrete-time systems. The parameter-dependent Lyapunov function approach and linear matrix inequality (LMI) technique are applied to solve the filtering problem. By considering auxiliary slack variables with free structure and introducing additional scalar parameters, new sufficient conditions for H∞ filter design are presented in terms of linear matrix inequalities (LMIs), which guarantee the filtering error systems to be asymptotically stable with prescribed H∞ performances. In contrast to the existing results for H∞ filter design, the new proposed design method can provide less conservative results. Numerical examples are provided to demonstrate the effectiveness of the proposed method.