Robust stochastic stability and H∞ performance for a class of uncertain impulsive stochastic systems

In this paper, we discuss the problem of robust stochastic stability and H∞ performance for a class of uncertain impulsive stochastic systems under sampled measurements. The parameter uncertainties are assumed to be time-varying and value-bounded. We give a sufficient condition in terms of certain linear matrix inequalities (LMIs) to guarantee the uncertain impulsive stochastic system to be robustly stochastically stable. Furthermore, we discuss a stochastically stable filter, using the locally sampled measurements, which ensures both the stochastic stability and a prescribed level of H∞ performance for the filtering error system for all admissible uncertainties. We give a sufficient condition for the existence of such a filter and an explicit expression of a desired filter if relevant conditions are satisfied.