State estimation of neural networks with two Markovian jumping parameters and multiple time delays

Abstract This paper studies the problem of state estimation for two Markovian jumping neural networks with leakage, discrete and distributed delays. The Markovian jumping parameters in connection weight matrices and discrete time-varying delay are assumed to be different. By constructing an appropriate Lyapunov–Krasovskii functional and combining with the reciprocally convex approach and Wirtinger-based integral inequality (this inequality gives a tighter upper bound), some sufficient conditions are established. They guarantee that the estimation error converges to zero exponentially in the mean square sense. Compared with existing results, the obtained criteria are more effective due to the application of Matrix decomposition method which sufficiently utilizes the information of Lyapunov matrices. Numerical examples and simulations are given to demonstrate the reduced conservatism and effectiveness of the proposed method.

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