Delayed Cellular Neural Networks Research Articles

New Criteria on Stability of Dynamic Memristor Delayed Cellular Neural Networks.

Dynamic memristor (DM)-cellular neural networks (CNNs), which replace a linear resistor with flux-controlled memristor in the architecture of each cell of traditional CNNs, have attracted researchers' attention. Compared with common neural networks, the DM-CNNs have an outstanding merit: when a steady state is reached, all voltages, currents, and power consumption of DM-CNNs disappeared, in the meantime, the memristor can store the computation results by serving as nonvolatile memories. The previous study on stability of DM-CNNs rarely considered time delay, while delay is quite common and highly impacts the stability of the system. Thus, taking the time delay effect into consideration, we extend the original system to DM-D(delay)CNNs model. By using the Lyapunov method and the matrix theory, some new sufficient conditions for the global asymptotic stability and global exponential stability with a known convergence rate of DM-DCNNs are obtained. These criteria generalized some known conclusions and are easily verified. Moreover, we find DM-DCNNs have 3n equilibrium points (EPs) and 2n of them are locally asymptotically stable. These results are obtained via a given constitutive relation of memristor and the appropriate division of state space. Combine with these theoretical results, the applications of DM-DCNNs can be extended to other fields, such as associative memory, and its advantage can be used in a better way. Finally, numerical simulations are offered to illustrate the effectiveness of our theoretical results.

Study on disturbance attenuation of cellular neural networks with time-varying delays

The paper is concerned with the problem of disturbance attenuating controller design for delayed cellular neural networks (DCNNs). Via combining four different states cases in DCNNs and applying Razumikhin function analysis, a feedback control law in the form of linear matrix inequality (LMI) is derived for guaranteeing disturbance attenuation of the closed systems. Finally, a numerical example of DCNNs is given to indicate the effectiveness of the proposed disturbance attenuating control. Because there is no restriction that the time derivative of the delay is smaller than 1 which is a hypothesis of many articles concerning time-varying delayed systems, the proposed scheme has significance impact on the design and applications of the disturbance attenuating control. Meanwhile an example of CNNs is offered to show the usefulness of the controller to the systems without time delay.

Global Exponential Stability for DCNNs with Impulses on Time Scales

A class of delayed cellular neural networks (DCNNs) with impulses on time scales is considered. By using the topological degree theory, and the time scale calculus theory some sufficient conditions are derived to ensure the existence, uniqueness, and global exponential stability of equilibria for this class of neural networks. Finally, a numerical example illustrates the feasibility of our results and also shows that the continuous-time neural network and the discrete-time analogue have the same dynamical behaviors. The results of this paper are completely new and complementary to the previously known results.

Delay-dependent global exponential robust stability for delayed cellular neural networks with time-varying delay

This paper investigates a class of delayed cellular neural networks (DCNN) with time-varying delay. Based on the Lyapunov–Krasovski functional and integral inequality approach (IIA), a uniformly asymptotic stability criterion in terms of only one simple linear matrix inequality (LMI) is addressed, which guarantees stability for such time-varying delay systems. This LMI can be easily solved by convex optimization techniques. Unlike previous methods, the upper bound of the delay derivative is taken into consideration, even if larger than or equal to 1. It is proven that results obtained are less conservative than existing ones. Four numerical examples illustrate efficacy of the proposed methods.

Disturbance Attenuating Control for Cellular Neural Networks with Time-Varying Delays

The problem of disturbance attenuating controller design for delayed cellular neural networks (DCNNs) is considered. Via combining four different states cases in DCNNs and applying Razumikhin function analysis, a feedback control law in the form of linear matrix inequality (LMI) is derived for guaranteeing disturbance attenuation of the closed systems. Finally, a numerical example of DCNNs is given to indicate the effectiveness of the proposed disturbance attenuating control.

Mean square exponential stability of stochastic delay cellular neural networks

Mean square exponential stability of stochastic delay cellular neural networks

Guaranteed Cost Control of Saturated Time-Varying Delay Systems

This paper mainly considers the control problem of saturated time-varying delay systems. Applying the saturation degree function and the convex hull theory to handle the saturated terms, we put forward the guaranteed cost controller of the system according to the Lyapunov-Krasovskii theorem. Then we make use of Schur complement to convert the QMI (quadratic matrix inequality) to a LMI (linear matrix inequality) and so it can be easily used as controller synthesis. Finally, we apply the guaranteed cost controller to a two dimentional time-varying delay cellular neural networks, and the simulation results show the effectiveness of the proposed controller.

Complete stability of cellular neural networks with unbounded time-varying delays

In this paper, we are concerned with the delayed cellular neural networks (DCNNs) in the case that the time-varying delays are unbounded. Under some conditions, it shows that the DCNNs can exhibit 3(n) equilibrium points. Then, we track the dynamics of u(t)(t>0) in two cases with respect to different types of subset regions in which u(0) is located. It concludes that every solution trajectory u(t) would converge to one of the equilibrium points despite the time-varying delays, that is, the delayed cellular neural networks are completely stable. The method is novel and the results obtained extend the existing ones. In addition, two illustrative examples are presented to verify the effectiveness of our results.

Guaranteed Cost Stabilization of Time-varying Delay Cellular Neural Networks via Riccati Inequality Approach

This letter deals with the guaranteed cost stabilization of time---varying delay cellular neural networks (DCNNs). Based on the Razumikhin theorem and via applying the zoned discussion and maximax synthesis method in DCNNs, the quadratic Riccati matrix inequality criterion for the guaranteed cost stabilization controller is designed to stabilize the given chaotic DCNNs. The minimization of the guaranteed cost of stabilization for the DCNNs is also given. Finally, numerical examples are given to show the effectiveness of proposed guaranteed cost stabilization control and its corresponding minimization problem.

Stability analysis of delayed cellular neural networks with impulsive effects

This paper focuses on the problem of exponential stability analysis of delayed cellular neural networks (DCNNs) with impulsive effects. The time delay is allowed to be time varying. By utilizing the piecewise linear property of the activation function of DCNNs and applying Razumikhin-type analysis techniques, two different types of delay-independent criteria for exponential stability of DCNNs with impulsive effects are derived in terms of linear matrix inequalities. The first of the two criteria can be used to design a reduced-order impulsive control law for unstable DCNNs. The other criterion shows that local stability of the equilibriums of the original DCNNs can still be retained under certain impulsive perturbation. Two numerical examples illustrated the efficiency of the proposed method.

Guaranteed Cost Synchronization of Chaotic Cellular Neural Networks with Time-Varying Delay

Synchronization of cellular neural networks with time-varying delay is discussed in this letter. Based on Razumikhin theorem, a guaranteed cost synchronous controller is given. Unlike Lyapunov-Krasovskii analysis process, there is no constraint on the change rate of time delay. The saturated terms emerging in the Razumikhin analysis are amplified by zoned discussion and maximax synthesis rather than by Lipschitz condition and vector inequality, which will bring more conservatism. Then the controller criterion is transformed from quadratic matrix inequality form into linear matrix inequality form, with the help of a sufficient and necessary transformation condition. The minimization of the guaranteed cost is studied, and a further criterion for getting the controller is presented. Finally, the guaranteed cost synchronous control and its corresponding minimization problem are illustrated with examples of chaotic time-varying delay cellular neural networks.

Guaranteed cost synchronous control of time-varying delay cellular neural networks

This paper deals with the synchronization of time-varying delay cellular neural networks. Based on the Lyapunov stability analysis and the zoned discussion and maximax synthesis (ZDMS) method, the quadratic matrix inequality (QMI) criterion for the guaranteed cost synchronous controller is designed to synchronize the given chaotic systems. For the convenience to solve, using a generalized result of Schur complement, the criterion in the form of QMI is turned into the linear matrix inequality (LMI) form, which can be used efficiently via existing numerical convex optimization algorithms such as the interior-point algorithms for solving LMIs. The minimization of the guaranteed cost is further studied, and the corresponding LMI criterion for getting the controller is given. Finally, numerical examples are given to show the effectiveness of proposed guaranteed cost synchronous control and its corresponding minimization problem.

Stability and Dissipativity Analysis of Distributed Delay Cellular Neural Networks

In this brief, the problems of delay-dependent stability analysis and strict (Q,S,ℜ)-α-dissipativity analysis are investigated for cellular neural networks (CNNs) with distributed delay. First, by introducing an integral partitioning technique, two new forms of Lyapunov-Krasovskii functionals are constructed, and improved distributed delay-dependent stability conditions are established in terms of linear matrix inequalities. Based on this criterion, a new sufficient delay and α-dependent condition is given to guarantee that the CNNs with distributed delay are strictly (Q,S,ℜ)-α-dissipative. The results developed in this brief can tolerate larger allowable delay than existing ones in the literature, which is demonstrated by several examples.

Exponential Stability of Solution for Delayed Cellular Neural Networks with Impulses

By using M-matrix theory, some inequality analysis technology and mathematical induction, some sufficient conditions are derived ensuring existence and global exponential stability of the equilibrium points of delayed cellular neural networks (DCNNS) with impulses. Without assuming the boundedness of signal functions, the results obtained have sufficient significance in design. Finally, an example with numerical simulation is given to show the effectiveness of the proposed method and results.

A New Method for Complete Stability Analysis of Cellular Neural Networks With Time Delay

This paper presents new complete stability results for delayed cellular neural networks (DCNNs). A novel method is proposed for complete stability analysis of DCNNs. By applying the M-matrix theory and introducing some new estimation techniques on the solutions of DCNNs, a simple and improved complete stability criterion is derived. The new criterion unifies the delay-dependent and delay-independent complete stability conditions for DCNNs. Moreover, the obtained delay-dependent criterion can give a larger upper bound of the time delay than the existing ones such that the complete stability can still be retained. Numerical examples are presented which show that the new complete stability results for DCNNs are compared favorably with the existing results.

New results on exponential attractivity of multiple almost periodic solutions of cellular neural networks with time-varying delays

We present new results on multi-almost periodicity and attractivity of delayed cellular neural networks (DCNNs). Some criteria are derived for ensuring locally or globally exponential attractivity of multiple almost periodic solutions in designated regions. It is shown that N -dimensional DCNNs can have a coexistence of 2 N locally attractive almost periodic solutions. Furthermore, the obtained conclusions have a wider applicable range, improve and complement the existing ones. Finally, computer simulations are given to show the effectiveness of the theoretical results.

Impulsive Stabilization of Delayed Cellular Neural Networks via Partial States

The problem of impulsive stabilization of delayed cellular neural networks (DCNNs) via partial states is discussed. The time delay is allowed to be time-varying. By utilizing the piecewise linear property of the activation function of DCNNs and applying piecewise differential Lyapunov combined with Razumikhin-type analysis techniques, a sufficient condition for the existence of the impulsive control law via partial states is derived. The sufficient condition is given in terms of linear matrix inequalities concerning the interconnection matrices and the bounds of the impulsive intervals. By using this result, an impulsive stabilization scheme for a class of DCNNs is proposed. The impulsive stabilization scheme only utilizes the output of partial states of the controlled DCNN. A numerical example illustrates the efficiency of the proposed method.

Stability analysis of delayed cellular neural networks with and without noise perturbation

The stability of a class of delayed cellular neural networks (DCNN) with or without noise perturbation is studied. After presenting a simple and easily checkable condition for the global exponential stability of a deterministic system, we further investigate the case with noise perturbation. When DCNN is perturbed by external noise, the system is globally stable. An important fact is that, when the system is perturbed by internal noise, it is globally exponentially stable only if the total noise strength is within a certain bound. This is significant since the stochastic resonance phenomena have been found to exist in many nonlinear systems.

Existence and global attractivity of almost periodic solution for DCNNs with time-varying coefficients

By using exponential dichotomy, the Banach fixed point theory and some inequality analysis technology, some sufficient conditions are derived ensuring existence, uniqueness and global attractivity of almost periodic solution of delayed cellular neural networks (DCNNs) with time-varying coefficients. Without assuming the boundedness of signal functions, the results obtained have sufficient significance in design and applications of almost periodic oscillatory DCNNs.

An Linear Matrix Inequality Approach to the Global Asymptotic Stability for DelayedCellular Neural Networks

An Linear Matrix Inequality Approach to the Global Asymptotic Stability for DelayedCellular Neural Networks