Robust Filtering for Nonlinear Stochastic Delay Systems with Multiplicative Noise and Jumps

In this paper, the robust H ∞ filtering problem of nonlinear stochastic systems with delay and infinite Markov jumps was studied. Based on a nonlinear stochastic bounded real lemma and the filtering equation, we constructed the asymptotically mean square H ∞ filtering and the exponentially mean square H ∞ filtering via solving Hamilton-Jacobi inequalities. A numerical example was given to show the effectiveness of the proposed results.