Resilient $$H_{\infty }$$ H ∞ Filtering for Stochastic Systems with Randomly Occurring Gain Variations, Nonlinearities and Channel Fadings

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In this paper, the resilient $$H_{\infty }$$ filtering problem for a class of stochastically uncertain discrete-time systems with randomly occurring gain variations, nonlinearities (RONs) and channel fadings is investigated. Considering the existences of random parameter fluctuations in both actual plant and filter, a sequence of mutually independent random variables with known probabilistic distribution is utilized to better describe the stochastic characteristics. The phenomenon RONs, which is regulated by random variables with Bernoulli distribution, is used to reflect the reality that actual systems are generally nonlinear. The system measurement with channel fadings is described by the stochastic Rice fading model, where the channel coefficients are a set of mutually independent random variables with any probability density function. It is worthwhile to mention that a series of slack matrix variables are exploited to eliminate the coupling between the plant matrices and the designed filter parameters by providing free dimensions in the solution space. The purpose of this paper is to design a resilient $$H_{\infty }$$ filter such that the filtering error system is asymptotically stable with a prescribed $$H_{\infty }$$ performance level. And sufficient conditions for filter design are eventually converted into solving a convex optimization problem over linear matrix inequalities. A numerical example is presented to illustrate effectiveness of the proposed approach.