Robust \(H_2/H_{\infty}\) filter design for a class of nonlinear stochastic systems with state-dependent noise (Q1955153)

Summary: We investigate the problem of robust filter design for a class of nonlinear stochastic systems with state-dependent noise. The state and measurement are corrupted by stochastic uncertain exogenous disturbance and the dynamic system is modeled by Itô-type stochastic differential equations. For this class of nonlinear stochastic systems, the robust \(H_{\infty}\) filter can be designed by solving linear matrix inequalities (LMIs). Moreover, a mixed \(H_2/H_\infty\) filtering problem is also solved by minimizing the total estimation error energy when the worst-case disturbance is considered in the design procedure. A numerical example is provided to illustrate the effectiveness of the proposed method.