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This paper addresses the resilient H∞$H_{\infty }$ state estimation problem under variance constraint for discrete uncertain time-varying recurrent neural networks with randomly varying nonlinearities and missing measurements. The phenomena of missing measurements and randomly varying nonlinearities are described by introducing some Bernoulli distributed random variables, in which the occurrence probabilities are known a priori. Besides, the multiplicative noise is employed to characterize the estimator gain perturbation. Our main purpose is to design a time-varying state estimator such that, for all missing measurements, randomly varying nonlinearities and estimator gain perturbation, both the estimation error variance constraint and the prescribed H∞$H_{\infty }$ performance requirement are met simultaneously by providing some sufficient criteria. Finally, the feasibility of the proposed variance-constrained resilient H∞$H_{\infty }$ state estimation method is verified by some simulations.

advances in difference equations

Variance-constrained resilient $H_{\infty }$ state estimation for time-varying neural networks with randomly varying nonlinearities and missing measurements