This paper investigates the robust stochastic stability and H∞ analysis for stochastic systems with time-varying delay and Markovian jump. By using the freeweighting matrix technique, i.e., He＇s technique, and a stochastic Lyapunov-Krasovskii functional, new delay-dependent criteria in terms of linear matrix inequalities are derived for the the robust stochastic stability and the H∞ disturbance attenuation. Three numerical examples axe given. The results show that the proposed method is efficient and much less conservative than the existing results in the literature.
In this paper we obtain some results on the global existence of solution to It5 stochastic impulsive differential equations in u（[0,∞）,Rn）which denotes the family of Rn-valued stochastic processes x satisfying supt∈[0,∞）E｜x（t）｜2〈∞ under non-Lipschitz coefficients. The Schaefer fixed point theorem is employed to achieve the desired result. An example is provided to illustrate the obtained results.
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.
