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State estimation for discrete-time Markovian jumping neural networks with mixed mode-dependent delays. (English) Zbl 1227.92002
Summary: We investigate the state estimation problem for a new class of discrete-time neural networks with Markovian jumping parameters as well as mode-dependent mixed time-delays. The parameters of the discrete-time neural networks are subject to switching from one mode to another at different times according to a Markov chain, and the mixed time-delays consist of both discrete and distributed delays that are dependent on the Markovian jumping mode. New techniques are developed to deal with the mixed time-delays in the discrete-time setting, and a novel Lyapunov-Krasovskii functional is put forward to reflect the mode-dependent time-delays. Sufficient conditions are established in terms of linear matrix inequalities (LMIs) that guarantee the existence of state estimators. We show that both the existence conditions and the explicit expression of the desired estimator can be characterized in terms of the solution to an LMI. A numerical example is exploited to show the usefulness of the derived LMI-based conditions.
MSC:
92B20General theory of neural networks (mathematical biology)
60J20Applications of Markov chains and discrete-time Markov processes on general state spaces
15A45Miscellaneous inequalities involving matrices
60J75Jump processes
62M05Markov processes: estimation
65C20Models (numerical methods)