L2–L∞ filtering for stochastic Markovian jump delay systems with nonlinear perturbations

• The nonlinearities in state and measurement equations in this paper are more general than those in the literature.
• A stochastic integral inequality is presented to establish the main results on L2–L∞L2–L∞ filtering for stochastic systems..
• The information of time-varying delay is reserved to reduce the conservatism.

This paper is concerned with the L2–L∞L2–L∞ filtering problem for Itô stochastic delayed Markovian jump systems subject to nonlinear parameter and sensor perturbations. The nonlinear perturbations in both state and measurement equations considered in the existing literature are generalizeed by including the cross information among the current state, the delayed state and the nonlinear perturbations. Based on a stochastic integral inequality and the convex analysis property, an L2–L∞L2–L∞ performance condition is presented to guarantee the mean-square exponential stability of the resulting filtering error system with prescribed L2–L∞L2–L∞ disturbance attenuation level. By utilizing the information of the time-varying delay, the delay is not estimated by the worst-case enlargement such that the conservatism is reduced. Then with the obtained performance analysis result, a stochastic L2–L∞L2–L∞ filter for the system under consideration is designed. Illustrative examples are given to demonstrate the usefulness of the developed approach.