Robust filtering for nonlinear stochastic systems with uncertainties and Markov delays

This paper investigates the H ∞ filtering problem for a class of general nonlinear stochastic systems considering model uncertainties and random time delays governed by Markov chains simultaneously. The general algebraic Hamilton–Jacobi inequality (HJI) is established first for general nonlinear stochastic systems with uncertainties and random Markovian delays. Then a set of sufficient conditions are derived for the filtering system to achieve stochastic stability in the sense of mean square and the prescribed disturbance attenuation level. Moreover, the developed results are specialized for a special class of nonlinear stochastic systems, by presenting the sufficient conditions in terms of matrix inequalities. Simulation results demonstrate the effectiveness of the proposed approach.