Cheng-De Zheng

Novel delay-dependent criteria for global robust exponential stability of delayed cellular neural networks with norm-bounded uncertainties

The problem ensuring the global robust exponential stability of a class of delayed cellular neural networks with norm-bounded uncertainties is studied. Without assuming the boundedness of the activation functions, by applying the idea of vector Lyapunov function and linear matrix inequality (LMI) techniques, some sufficient conditions for the global robust exponential stability of uncertain cellular neural networks and the existence, uniqueness, global exponential stability of cellular neural networks are obtained, which generalize the previous results in the literature. The criteria are easy to be verified, since they take the form of LMI. Three illustrative examples are given to demonstrate the effectiveness of the proposed results.

On Stabilization of Stochastic Cohen-Grossberg Neural Networks With Mode-Dependent Mixed Time-Delays and Markovian Switching

The globally exponential stabilization problem is investigated for a general class of stochastic Cohen-Grossberg neural networks with both Markovian jumping parameters and mixed mode-dependent time-delays. The mixed time-delays consist of both discrete and distributed delays. This paper aims to design a memoryless state feedback controller such that the closed-loop system is stochastically exponentially stable in the mean square sense. By introducing a new Lyapunov-Krasovskii functional that accounts for the mode-dependent mixed delays, stochastic analysis is conducted in order to derive delay-dependent criteria for the exponential stabilization problem. Three numerical examples are carried out to demonstrate the feasibility of our delay-dependent stabilization criteria.

Improved Robust Stability Criteria for Delayed Cellular Neural Networks via the LMI Approach

Uniqueness and robust exponential stability are analyzed for a class of uncertain cellular neural networks with time-varying delays. By dividing the variation interval of the time delay into two subintervals with equal length, a novel Lyapunov-Krasovskii functional is introduced. Using the free-weighting matrix method, a new delay-dependent stability criterion is obtained, which is less conservative than some previous literature. Since the result is presented in terms of linear matrix inequalities, the condition is easy to be verified. Finally, an example is given to illustrate the effectiveness of our proposed method.

Novel Exponential Stability Criteria of High-Order Neural Networks With Time-Varying Delays

The global exponential stability is analyzed for a class of high-order Hopfield-type neural networks with time-varying delays. Based on the Lyapunov stability theory, together with the linear matrix inequality approach and free-weighting matrix method, some less conservative delay-independent and delay-dependent sufficient conditions are presented for the global exponential stability of the equilibrium point of the considered neural networks. Two numerical examples are provided to demonstrate the effectiveness of the proposed stability criteria.

Less conservative results of state estimation for delayed neural networks with fewer LMI variables

In this paper, the state estimation problem is investigated for neural networks with time-varying delays as well as general activation functions. By applying the Finslers Lemma and constructing appropriate Lyapunov-Krasovskii functional based on delay partitioning, several improved delay-dependent conditions are developed to estimate the neuron state with some available output measurements such that the error-state system is global asymptotically stable. It is established theoretically that one special case of the obtained criteria is equivalent to some existing result with same conservatism but including fewer LMI variables. As the present conditions involve no free-weighting matrices, the computational burden is largely reduced. Two examples are provided to demonstrate the effectiveness of the theoretical results.

New LMT-based delay-dependent criterion for global asymptotic stability of cellular neural networks

The problem of global asymptotic stability analysis is studied for a class of cellular neural networks with time-varying delay. By defining a Lyapunov-Krasovskii functional, a new delay-dependent stability condition is derived in terms of linear matrix inequalities. The obtained criterion is less conservative than some previous literature because free-weighting matrix method and the Jensen integral inequality are considered. Three illustrative examples are given to demonstrate the effectiveness of the proposed results.

Stability analysis of mixed recurrent neural networks with time delay in the leakage term under impulsive perturbations

This paper investigates a class of mixed recurrent neural networks with time delay in the leakage term under impulsive perturbations. The mixed time-delays consist of both discrete and distributed delays. By using the Lyapunov functional method, linear matrix inequality approach and general convex combination technique, two novel sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point of the networks. The proposed results, which do not require the boundedness, differentiability and monotonicity of the activation functions, can be easily checked via Matlab software. Moreover, they indicate that the stability behavior of neural networks is very sensitive to the time delay in the leakage term. Finally, numerical examples are given to demonstrate the effectiveness of our theoretical results.

An Augmented LKF Approach Involving Derivative Information of Both State and Delay

An augmented Lyapunov-Krasovskii functional (LKF) approach is presented to derive sufficient conditions for the existence, uniqueness, and globally exponential stability of the equilibrium point of a class of cellular neural networks with time-varying delays. By dividing the variation interval of the time delay into several subintervals with equal length, a novel vector LKF is introduced and new conditions are obtained based on the homeomorphism mapping principle, free-weighting matrix method, and linear matrix inequality techniques. Since the criteria are involving derivative information of both state and delay, the obtained results are less conservative than some previous ones. Two examples are also given to show the effectiveness of the presented criteria.

Novel delay-dependent stability criteria for switched Hopfield neural networks of neutral type

This paper investigates the stability of switched Hopfield neural networks of neutral type with time-varying delay and continuously distributed delay. By using the quadratic convex combination method, the reciprocal convex combination approach, some generalized Jensen integral inequalities, and the free-weight matrix method, several novel sufficient conditions are derived to ensure the asymptotic stability of the equilibrium point of the considered networks. The proposed results, which do not require the differentiability of the activation functions, can be easily checked via Matlab software. Finally, three numerical examples are given to demonstrate the effectiveness and less conservativeness of our theoretical results over existing literature.

Global Stability of Fuzzy Cellular Neural Networks with Mixed Delays and Leakage Delay Under Impulsive Perturbations

This paper investigates the global asymptotic stability of a kind of fuzzy cellular neural networks with mixed delays under impulsive perturbations. The mixed delays include constant delay in the leakage term (i.e., “leakage delay”), time-varying delays, and continuously distributed delays. By using the quadratic convex combination method, reciprocal convex approach, Jensen integral inequality, and linear convex combination technique, several novel sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point of the considered networks. The proposed results, which do not require the differentiability and monotonicity of the activation functions, can be easily checked via Matlab software. Finally, two numerical examples are given to demonstrate the effectiveness and less conservativeness of our theoretical results over existing literature.