Robust H∞ filtering for nonlinear stochastic systems

This paper describes the robust H_∞ filtering analysis and synthesis of nonlinear stochastic systems with state and exogenous disturbance-dependent noise. We assume that the state and measurement are corrupted by stochastic uncertain exogenous disturbance and that the system dynamic is modeled by Itoˆ-type stochastic differential equations. For general nonlinear stochastic systems, the H_∞ filter can be obtained by solving second-order nonlinear Hamilton-Jacobi inequalities. When the worst-case disturbance is considered in the design procedure, a mixed H₂/H_∞ filtering problem is also solved by minimizing the total estimation error energy. It is found that for a class of special nonlinear stochastic systems, the H_∞ filtering design can be given via solving several linear matrix inequalities instead of Hamilton-Jacobi inequalities. A few examples show that the proposed methods are effective.