Robust filtering for discrete time piecewise impulsive systems

This paper investigates the filtering problems for the discrete time piecewise impulsive system. First, the robust H∞ filtering problem and generalized H2 filtering problem for the discrete time piecewise impulsive system are introduced. Then, linear matrix inequality (LMI) conditions are proposed for the design of H∞ and generalized H2 filters such that the resulting discrete time piecewise impulsive filtering error system is globally stable with guaranteed H∞ or H2 performance. Finally, a numerical simulation is also given to illustrate the effectiveness of the proposed approaches.