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Finite-time H∞ filtering of time-delay stochastic jump systems with unbiased estimation

Abstract This paper is concerned with the problem of unbiased stochastic finite-time H∞ filtering for a class of Markov jump systems with constant time-delays. The filtering error dynamics is constructed based on an H∞ filter with unbiased estimation condition. The objective is to design such an unbiased filter that the finite-time L2 gain from the unknown input to an estimation error is minimized or guaranteed to be less than or equal to a prescribed value. By using the stochastic Lyapunov–Krasovskii functional approach, sufficient conditions are obtained for the existence of the desired unbiased H∞ filter, which also guarantees the stochastic finite-time boundedness of the filtering error dynamic systems. The design criteria are presented in the form of linear matrix inequalities and described as the optimization algorithms. Finally, two numerical examples are employed to illustrate the effectiveness of the developed techniques.