This paper studies the mixed $H_-/H_{ \infty}$ fault detection filtering of It\^o-type nonlinear stochastic systems. Mixed $H_-/H_{ \infty}$ filtering combines the system robustness to the external disturbance and the sensitivity to the fault of the residual signal. Firstly, for It\^o-type affine nonlinear stochastic systems, some sufficient criteria are obtained for the existence of $H_-/H_{ \infty}$ filter in terms of Hamilton-Jacobi inequalities (HJIs). Secondly, for a class of quasi-linear It\^o systems, a sufficient condition is given for the existence of $H_-/H_{ \infty}$ filter by means of linear matrix inequalities (LMIs). Finally, a numerical example is presented to illustrate the effectiveness of the proposed results.
Categories: math.OC