Robust H∞ filtering for nonlinear stochastic state-delayed systems

This note studies the robust H_infin filtering problem of nonlinear stochastic systems with state-delay appearing in state equation, measurement and controlled output, where the state is governed by a stochastic Ito-type equation. Based on a nonlinear stochastic bounded real lemma and an exponential estimate formula, an exponential (asymptotic) mean square H_infin filtering design of nonlinear stochastic time-delay systems is presented via solving a Hamilton-Jacobi inequality. As one corollary, for linear stochastic time-delay systems, a Luenberger-type filter is obtained by solving a linear matrix inequality. Two simulation examples are finally given to show the effectiveness of our results.