Abstract: This paper investigates robust filter design for linear discrete-time impulsive systems with uncertainty under H_∝ performance. First, an impulsive linear filter and a robust H_∝ filtering problem are introduced for a discrete-time impulsive systems. Then, a sufficient condition of asymptotical stability and H_∝ performance for the filtering error systems are provided by the discrete-time Lyapunov function method. The filter gains can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, a numerical example is presented to show effectiveness of the obtained result.

Key words: discrete-time, impulses, robust H_∝ filtering, linear matrix inequalities