Stochastic input-to-state stability and filtering for a class of stochastic nonlinear systems

In this paper, an H?H? filtering problem is considered for a class of stochastic nonlinear systems with time-delay and exogenous disturbances. Sufficient conditions for stochastic input-to-state stability (SISS) of the stochastic nonlinear systems are developed via Lyapunov function method and linear matrix inequalities (LMIs) technique. The purpose of this work is to design a nonlinear filter to ensure both the SISS and a prescribed H?H? attenuation level for the corresponding filtering error system. By using the SISS results, a set of sufficient conditions for the existence of H?H? filter is given in the form of LMI. When the LMI is feasible, an explicit expression of a desired filter is presented. Finally, some numerical and practical examples are employed to demonstrate the effectiveness of the proposed approaches.