Unbiased estimation of Markov jump systems with distributed delays

• Sufficient conditions are obtained for the unbiased H∞ filtering scheme to a class of Markov jump systems (MJSs) with distributed time-delays.
• The filtering error dynamic MJSs is guaranteed to be stochastically stable and satisfies a prescribed level of H∞ disturbance attenuation in an infinite time-interval.
• The design method is presented in the form of linear matrix inequalities techniques, and then described as an optimization problem.
• Two numerical simulations are given to illustrate the performance of the proposed approach.

The unbiased H∞ filtering problem is considered for a class of Markov jump systems (MJSs) with distributed time-delays. Based on the selected Lyapunov–Krasovskii functional, it gives a sufficient condition for the existence of the mode-dependent unbiased H∞ filter such that the filtering error dynamic MJSs is stochastically stable and satisfies a prescribed level of H∞ disturbance attenuation in an infinite time-interval. The design criterions are presented in the form of linear matrix inequality techniques, and then are described as the optimization problems. At last, two numerical examples are employed to illustrate the effectiveness of the developed techniques.