Event-Triggered $H_\infty$ State Estimation for Delayed Stochastic Memristive Neural Networks With Missing Measurements: The Discrete Time Case

In this paper, the event-triggered <inline-formula> <tex-math notation="LaTeX">$H_\infty $ </tex-math></inline-formula> state estimation problem is investigated for a class of discrete-time stochastic memristive neural networks (DSMNNs) with time-varying delays and missing measurements. The DSMNN is subject to both the additive deterministic disturbances and the multiplicative stochastic noises. The missing measurements are governed by a sequence of random variables obeying the Bernoulli distribution. For the purpose of energy saving, an event-triggered communication scheme is used for DSMNNs to determine whether the measurement output is transmitted to the estimator or not. The problem addressed is to design an event-triggered <inline-formula> <tex-math notation="LaTeX">$H_\infty $ </tex-math></inline-formula> estimator such that the dynamics of the estimation error is exponentially mean-square stable and the prespecified <inline-formula> <tex-math notation="LaTeX">$H_\infty $ </tex-math></inline-formula> disturbance rejection attenuation level is also guaranteed. By utilizing a Lyapunov–Krasovskii functional and stochastic analysis techniques, sufficient conditions are derived to guarantee the existence of the desired estimator, and then, the estimator gains are characterized in terms of the solution to certain matrix inequalities. Finally, a numerical example is used to demonstrate the usefulness of the proposed event-triggered state estimation scheme.

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