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In this paper, the H ∞ filtering problem is investigated for a class of discrete-time arbitrary switched neural networks with missing measurements, stochastic perturbations, and communication delays. Based on the average dwell time approach and a set of Kronecker delta functions, a unified measurement model is established to represent the phenomena of missing measurements, time delays and nonlinearities. The aim of this paper is to design an H ∞ filter such that the filter error dynamics is exponentially mean-square stable and the H ∞ performance requirement is satisfied simultaneously. By using the Lyapunov stability theory and the matrix technology, the design method of the desired filter is given in terms of a matrix inequality which can be solved by using the available software. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper investigates the almost sure H ∞ sliding mode control (SMC) problem for nonlinear stochastic systems with Markovian switching and time-delays. An integral sliding surface is first constructed for the addressed system. Then, by employing the stopping time method combined with martingale inequalities, sufficient conditions are established to ensure the almost surely exponential stability and the H ∞ performance of the system dynamics in the specified sliding surface. A SMC law is designed to guarantee the reachability of the specified sliding surface almost surely. Furthermore, the obtained results are applied to a class of special nonlinear stochastic systems with Markovian switching and time-delays, where the desired SMC law is obtained in terms of the solutions to a set of matrix inequalities. Finally, a numerical example is given to show the effectiveness of the proposed SMC scheme. [ABSTRACT FROM AUTHOR]