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In this paper, we study the robust H∞ filtering problem for a class of nonhomogeneous Markovian jump delay systems (NMJDSs) with an N-step-ahead Lyapunov-Krasovskii functional (NALKF) approach. The N-step-ahead approach is utilized to reduce the conservatism of robust H∞ filtering. We aim to design filters such that, for all possible time-varying transition probabilities and all admissible parameter uncertainties and time-delays, the filtering error system is mean-square stable with a smaller estimated error and a lower dissipative level. In terms of linear matrix inequalities, sufficient conditions for the solvability of the addressed problem are developed via a moving horizon method. An illustrative example is included to elucidate advantages of the developed results and the practical potential of NALKF approach for NMJDSs.

Robust H∞ Filtering of Nonhomogeneous Markovian Jump Delay Systems via N-Step-Ahead Lyapunov-Krasovskii Functional Approach