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The state estimation problem is considered for a class of discrete-time stochastic neural networks with Markovian jumping parameters in this paper. Norm-bounded parameter uncertainties in the state and measurement equation and time-varying delays are investigated. The neuron activation function satisfies sector-bounded conditions, and the nonlinear perturbation of the measurement equation satisfies standard Lipschitz condition and sectorbounded conditions. By constructing proper LyapunovKrasovskii functional, delay-dependent conditions are developed in terms of linear matrix inequalities (LMIs) to estimate the neuron state such that the dynamic of the estimation error system is asymptotically stable. Finally, numerical examples are shown to demonstrate the effectiveness and applicability of the proposed design method.

In this paper, the robust non-fragile stabilisation and H∞ control problem is investigated for a class of uncertain discrete-time stochastic systems with Markovian jumping parameters and time-varying delay. The parameter uncertainties are supposed to be time-varying as well as norm-bounded. The aim of the robust non-fragile stabilisation problem is to design a non-fragile state feedback controller which guarantees the robust stability of the closed-loop system for all admissible uncertainties. At the same time, in addition to the robust stability requirement, a prescribed H∞ performance level is required to be achieved for the robust H∞ control problem. By Lyapunov stability theory, delay-segment-dependent conditions for the solvability of these problems are formulated in terms of linear matrix inequality technique. Finally, numerical examples are shown to demonstrate the usefulness and applicability of the proposed design method.