Uncertain Discrete-time Stochastic Neural Networks Research Articles

Robust Output Feedback Stabilization for Uncertain Discrete-Time Stochastic Neural Networks with Time-Varying Delay

This paper investigates the problem of robust exponential stabilization of uncertain discrete-time stochastic neural networks with time-varying delay based on output feedback control. By choosing an augmented Lyapunov–Krasovskii functional, we established the sufficient conditions of the delay-dependent asymptotical stabilization in the mean square for a class of discrete-time stochastic neural networks with time-varying delay. Furthermore, we obtain the criteria of robust global exponential stabilization in the mean square for uncertain discrete-time stochastic neural networks with time-varying delay. Finally, we give numerical examples to illustrate the effectiveness of the proposed results.

Robust $$H_\infty$$ H ∞ filtering for uncertain discrete-time stochastic neural networks with Markovian jump and mixed time-delays

In this paper, the robust $$H_\infty$$ filtering problem is discussed for a class of uncertain discrete-time stochastic neural networks with Markovian jumping parameters and mixed time-delays. Norm-bounded parameter uncertainties exist in both the state and measurement equation. The neuron activation function satisfies sector-bounded condition. The aim is to design a full-order filter with a prescribed $$H_\infty$$ performance level. Delay-segment-dependent conditions are developed in terms of linear matrix inequalities (LMIs) such that the resulted filtering error systems robustly stochastically stable. Finally, example is provided to demonstrate the effectiveness and applicability of the related results are obtained in this paper.

Robustly Exponential Stability Analysis for Discrete-Time Stochastic Neural Networks with Interval Time-Varying Delays

This paper deals with the problems of the global exponential stability and stabilization for a class of uncertain discrete-time stochastic neural networks with interval time-varying delay. By using the linear matrix inequality method and the free-weighting matrix technique, we construct a new Lyapunov–Krasovskii functional and establish new sufficient conditions to guarantee that the uncertain discrete-time stochastic neural networks with interval time-varying delay are globally exponential stable in the mean square. Furthermore, we extend our consideration to the stabilization problem for a class of discrete-time stochastic neural networks. Based on the state feedback control law, some novel delay-dependent criteria of the robust exponential stabilization for a class of discrete-time stochastic neural networks with interval time-varying delay are established. The controller gains are designed to ensure the global robust exponential stability of the closed-loop systems. Finally, numerical examples illustrate the effectiveness of the theoretical results we have obtained.

State estimation for uncertain discrete-time stochastic neural networks with Markovian jump parameters and time-varying delays

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 sector-bounded conditions. By constructing proper Lyapunov–Krasovskii 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.

Improved stochastic dissipativity of uncertain discrete-time neural networks with multiple delays and impulses

This paper investigates the problem of global dissipativity and global exponential dissipativity for a class of uncertain discrete-time stochastic neural networks with multiple time-varying delays. Here the multiple time-varying delays are assumed to be discrete and distributed and the uncertainties are assumed to be time-varying norm-bounded parameter uncertainties. By choosing a novel Lyapunov functional, combining with linear matrix inequality technique (LMI), Jensen’s inequality and stochastic analysis method, a new delay-dependent global dissipativity criterion is obtained in the form of LMI, which can be easily verified numerically using the effective LMI toolbox in Matlab. One important feature presents in our paper is that without employing model transformation and free weighting matrices our obtained result leads to less conservatism. Two illustrative examples are given to show the usefulness of the obtained dissipativity conditions.

Novel Delay-Dependent Stability Criteria for Uncertain Discrete-Time Stochastic Neural Networks with Time-Varying Delays

This paper investigates the problem of exponential stability for a class of uncertain discrete-time stochastic neural network with time-varying delays. By constructing a suitable LyapunovKrasovskii functional, combining the stochastic stability theory, the free-weighting matrix method, a delay-dependent exponential stability criteria is obtained in term of LMIs. Compared with some previous results, the new conditions obtain in this paper are less conservative. Finally, two numerical examples are exploited to show the usefulness of the results derived. Keywords—Delay-dependent stability; Neural networks; Timevarying delay; Linear matrix inequality(LMI).

Global dissipativity of uncertain discrete-time stochastic neural networks with time-varying delays

In this letter, the problem on global exponential dissipativity in mean is investigated for uncertain discrete-time stochastic neural networks with time-varying delays. In the concerned model, the stochastic disturbance is described by the Brownian motion, and the time-varying delays in a given range. By constructing appropriate Lyapunov–Krasovskii functional (LKF), combining with Jensen's inequality, stochastic analysis method and the free-weighting matrix method, a new delay-dependent global dissipativity criteria is obtained in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in Matlab. Finally, three examples are exploited to show the usefulness of the results derived.

Robust H∞ control for uncertain discrete-time stochastic neural networks with time-varying delays

In the last few years, the H∞ control problem has attracted much attention because of its both practical and theoretical importance. This study presents a robust H∞ control design approach for a class of uncertain discrete-time stochastic neural networks with time-varying delays. The neural network under consideration is subject to time-varying and norm bounded parameter uncertainties. For the robust stabilisation problem, a state feedback controller is designed to ensure global robust stability of the closed-loop form of neural network about its equilibrium point for all admissible uncertainties. In addition, to the requirement of the global robust stability, a prescribed H∞ performance level for all delays to satisfy both the lower bound and upper bound of the interval time-varying delay is required to be obtained. Through construction of a new Lyapunov–Krasovskii functional, a robust H∞ control scheme is presented in terms of linear matrix inequalities (LMIs). The controller gains can be derived by solving a set of LMIs. Finally, numerical examples with simulation results are given to illustrate the effectiveness of the developed theoretical results.

Stability analysis for discrete-time stochastic neural networks with mixed time delays and impulsive effects

This paper investigates the stability issues for a class of discrete-time stochastic neural networks with mixed time delays and impulsive effects. By constructing a new Lyapunov–Krasovskii functional and combining with the linear matrix inequality (LMI) approach, a novel set of sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point for the addressed discrete-time neural networks. Then the result is extended to address the problem of robust stability of uncertain discrete-time stochastic neural networks with impulsive effects. One important feature in this paper is that the stability of the equilibrium point is proved under mild conditions on the activation functions, and it is not required to be differentiable or strictly monotonic. In addition, two numerical examples are provided to show the effectiveness of the proposed method, while being less conservative.

New passivity results for uncertain discrete-time stochastic neural networks with mixed time delays

This paper investigates the problem of passivity analysis for a class of uncertain discrete-time stochastic neural networks with mixed time delays. Here the mixed time delays are assumed to be discrete and distributed time delays and the uncertainties are assumed to be time-varying norm-bounded parameter uncertainties. By constructing a novel Lyapunov functional and introducing some appropriate free-weighting matrices, delay-dependent passivity analysis criteria are derived. Furthermore, the additional useful terms about the discrete time-varying delay will be handled by estimating the upper bound of the derivative of Lyapunov functionals, which is different from the existing passivity results. These criteria can be developed in the frame of convex optimization problems and then solved via standard numerical software. Finally, a numerical example is given to demonstrate the effectiveness of the proposed results.

Robust state estimation for discrete-time stochastic neural networks with probabilistic measurement delays

In this paper, the robust H ∞ state estimation problem is investigated for a general class of uncertain discrete-time stochastic neural networks with probabilistic measurement delays. The measurement delays of the neural networks are described by a binary switching sequence satisfying a conditional probability distribution. The neural network under study involves parameter uncertainties, stochastic disturbances and time-varying delays, and the activation functions are characterized by sector-like nonlinearities. The problem addressed is the design of a full-order state estimator, for all admissible uncertainties, nonlinearities and time-delays, the dynamics of the estimation error is constrained to be robustly exponentially stable in the mean square and, at the same time, a prescribed H ∞ disturbance rejection attenuation level is guaranteed. By using the Lyapunov stability theory and stochastic analysis techniques, sufficient conditions are first established to ensure the existence of the desired estimators. These conditions are dependent on the lower and upper bounds of the time-varying delays. Then, the explicit expression of the desired estimator gains is described in terms of the solution to a linear matrix inequality (LMI). Finally, a numerical example is exploited to show the usefulness of the results derived.