Exponential Stability for Neutral Stochastic Markov Systems With Time-Varying Delay and Its Applications

The combined Lyapunov functionals method for stability analysis of neutral Cohen-Grossberg neural networks with multiple delays

This research article will employ the combined Lyapunov functionals method to deal with stability analysis of a more general type of Cohen-Grossberg neural networks which simultaneously involve constant time and neutral delay parameters. By utilizing some combinations of various Lyapunov functionals, we determine novel criteria ensuring global stability of such a model of neural systems that employ Lipschitz continuous activation functions. These proposed results are totally stated independently of delay terms and they can be completely characterized by the constants parameters involved in the neural system. By making some detailed analytical comparisons between the stability results derived in this research article and the existing corresponding stability criteria obtained in the past literature, we prove that our proposed stability results lead to establishing some sets of stability conditions and these conditions may be evaluated as different alternative results to the previously reported corresponding stability criteria. A numerical example is also presented to show the applicability of the proposed stability results.

Multistability and Robustness of Competitive Neural Networks With Time-Varying Delays

This article is devoted to analyzing the multistability and robustness of competitive neural networks (NNs) with time-varying delays. Based on the geometrical structure of activation functions, some sufficient conditions are proposed to ascertain the coexistence of equilibrium points, of them are locally exponentially stable, where represents a dimension of system and is the parameter related to activation functions. The derived stability results not only involve exponential stability but also include power stability and logarithmical stability. In addition, the robustness of stable equilibrium points is discussed in the presence of perturbations. Compared with previous papers, the conclusions proposed in this article are easy to verify and enrich the existing stability theories of competitive NNs. Finally, numerical examples are provided to support theoretical results.

Multimode function multistability for Cohen-Grossberg neural networks with mixed time delays

In this paper, we are concerned with the multimode function multistability for Cohen-Grossberg neural networks (CGNNs) with mixed time delays. It is introduced the multimode function multistability as well as its specific mathematical expression, which is a generalization of multiple exponential stability, multiple polynomial stability, multiple logarithmic stability, and asymptotic stability. Also, according to the neural network (NN) model and the maximum and minimum values of activation functions, n pairs of upper and lower boundary functions are obtained. Via the locations of the zeros of the n pairs of upper and lower boundary functions, the state space is divided into ∏_i=1ⁿ(2H_i+1) parts correspondingly. By virtue of the reduction to absurdity, continuity of function, Brouwer's fixed point theorem and Lyapunov stability theorem, the criteria for multimode function multistability are acquired. Multiple types of multistability, including multiple exponential stability, multiple polynomial stability, multiple logarithmic stability, and multiple asymptotic stability, can be achieved by selecting different types of function P(t). Two numerical examples are offered to substantiate the generality of the obtained criteria over the existing results.

Fuzzy SMC for Quantized Nonlinear Stochastic Switching Systems With Semi-Markovian Process and Application

This article is concerned with the issue of quantized sliding-mode control (SMC) design methodology for nonlinear stochastic switching systems subject to semi-Markovian switching parameters, T-S fuzzy strategy, uncertainty, signal quantization, and nonlinearity. Compared with the previous literature, the quantized control input is first considered in studying T-S fuzzy stochastic switching systems with a semi-Markovian process. A mode-independent sliding surface is adopted to avoid the potential repetitive jumping effects. Then, by means of the Lyapunov function, stochastic stability criteria are proposed to be dependent of sojourn time for the corresponding sliding-mode dynamics. Furthermore, the fuzzy-model-based SMC law is proposed to ensure the finite-time reachability of the sliding-mode dynamics. Finally, an application example of a modified series dc motor model is provided to demonstrate the effectiveness of the theoretical findings.

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.

General Decay Stability for Nonautonomous Neutral Stochastic Systems With Time-Varying Delays and Markovian Switching

A new type of asymptotic stability for nonlinear hybrid neutral stochastic systems with constant delays was investigated recently, where the criteria depended on the delays' sizes. Unfortunately, developed theory so far is not sufficient to deal with challenging problems of the decay rate, time-varying delays, and nonautonomous issues. These problems have not been tackled in the existing literature. Consequently, under the weak constraints, this article focuses on the general decay, including the exponential stability and the polynomial stability, for nonlinear nonautonomous hybrid neutral stochastic systems with time-varying delays by the approach of the multiple degenerate functionals. Moreover, this article derives the interesting assertions related to the general H_∞ stability and the polynomial growth at most.

Robust Stability of Recurrent Neural Networks With Time-Varying Delays and Input Perturbation

This paper addresses the robust stability of recurrent neural networks (RNNs) with time-varying delays and input perturbation, where the time-varying delays include discrete and distributed delays. By employing the new ψ -type integral inequality, several sufficient conditions are derived for the robust stability of RNNs with discrete and distributed delays. Meanwhile, the robust boundedness of neural networks is explored by the bounded input perturbation and L¹ -norm constraint. Moreover, RNNs have a strong anti-jamming ability to input perturbation, and the robustness of RNNs is suitable for associative memory. Specifically, when input perturbation belongs to the specified and well-characterized space, the results cover both monostability and multistability as special cases. It is revealed that there is a relationship between the stability of neural networks and input perturbation. Compared with the existing results, these conditions proposed in this paper improve and extend the existing stability in some literature. Finally, the numerical examples are given to substantiate the effectiveness of the theoretical results.

An improved Lyapunov functional with application to stability of Cohen-Grossberg neural networks of neutral-type with multiple delays

The essential objective of this research article is to investigate stability issue of neutral-type Cohen-Grossberg neural networks involving multiple time delays in states of neurons and multiple neutral delays in time derivatives of states of neurons in the network. By exploiting a modified and improved version of a previously introduced Lyapunov functional, a new sufficient stability criterion is obtained for global asymptotic stability of Cohen-Grossberg neural networks of neutral-type possessing multiple delays. The proposed new stability condition does not involve the time and neutral delay parameters. The obtained stability criterion is totally dependent on the system elements of Cohen-Grossberg neural network model. Moreover, the validity of this novel global asymptotic stability condition may be tested by only checking simple appropriate algebraic equations established within the parameters of the considered neutral-type neural network. In addition, an instructive numerical example is presented to indicate the advantages of our proposed stability result over the existing literature results obtained for stability of various classes of neutral-type neural networks having multiple delays.

Finite-Time Stability of Delayed Memristor-Based Fractional-Order Neural Networks

This paper studies one type of delayed memristor-based fractional-order neural networks (MFNNs) on the finite-time stability problem. By using the method of iteration, contracting mapping principle, the theory of differential inclusion, and set-valued mapping, a new criterion for the existence and uniqueness of the equilibrium point which is stable in finite time of considered MFNNs is established when the order α satisfies . Then, when , on the basis of generalized Gronwall inequality and Laplace transform, a sufficient condition ensuring the considered MFNNs stable in finite time is given. Ultimately, simulation examples are proposed to demonstrate the validity of the results.

New criteria for global stability of neutral-type Cohen-Grossberg neural networks with multiple delays

The significant contribution of this paper is the addressing the stability issue of neutral-type Cohen-Grossberg neural networks possessing multiple time delays in the states of the neurons and multiple neutral delays in time derivative of states of the neurons. By making the use of a novel and enhanced Lyapunov functional, some new sufficient stability criteria are presented for this model of neutral-type neural systems. The obtained stability conditions are completely dependent of the parameters of the neural system and independent of time delays and neutral delays. A constructive numerical example is presented for the sake of proving the key advantages of the proposed stability results over the previously reported corresponding stability criteria for Cohen-Grossberg neural networks of neutral type. Since, stability analysis of Cohen-Grossberg neural networks involving multiple time delays and multiple neutral delays is a difficult problem to overcome, the investigations of the stability conditions of the neutral-type the stability analysis of this class of neural network models have not been given much attention. Therefore, the stability criteria derived in this work can be evaluated as a valuable contribution to the stability analysis of neutral-type Cohen-Grossberg neural systems involving multiple delays.

Nonfragile Dissipative Synchronization for Markovian Memristive Neural Networks: A Gain-Scheduled Control Scheme

In this paper, the dissipative synchronization control problem for Markovian jump memristive neural networks (MNNs) is addressed with fully considering the time-varying delays and the fragility problem in the process of implementing the gain-scheduled controller. A Markov jump model is introduced to describe the stochastic changing among the connection of MNNs and it makes the networks under consideration suitable for some actual circumstances. By utilizing some improved integral inequalities and constructing a proper Lyapunov-Krasovskii functional, several delay-dependent synchronization criteria with less conservatism are established to ensure the dynamic error system is strictly stochastically dissipative. Based on these criteria, the procedure of designing the desired nonfragile gain-scheduled controller is established, which can well handle the fragility problem in the process of implementing the controller. Finally, an illustrated example is employed to explain that the developed method is efficient and available.

Global Anti-Synchronization of Complex-Valued Memristive Neural Networks With Time Delays

This paper formulates a class of complex-valued memristive neural networks as well as investigates the problem of anti-synchronization for complex-valued memristive neural networks. Under the concept of drive-response, several sufficient conditions for guaranteeing the anti-synchronization are given by employing suitable Lyapunov functional and some inequality techniques. The proposed results of this paper are less conservative than existing literatures due to the characteristics of memristive complex-valued neural networks. Moreover, the proposed results are easy to be validated with the parameters of system itself. Finally, two examples with numerical simulations are showed to demonstrate the efficiency of our theoretical results.

Multistability of Delayed Hybrid Impulsive Neural Networks With Application to Associative Memories

The important topic of multistability of continuous-and discrete-time neural network (NN) models has been investigated rather extensively. Concerning the design of associative memories, multistability of delayed hybrid NNs is studied in this paper with an emphasis on the impulse effects. Arising from the spiking phenomenon in biological networks, impulsive NNs provide an efficient model for synaptic interconnections among neurons. Using state-space decomposition, the coexistence of multiple equilibria of hybrid impulsive NNs is analyzed. Multistability criteria are then established regrading delayed hybrid impulsive neurodynamics, for which both the impulse effects on the convergence rate and the basins of attraction of the equilibria are discussed. Illustrative examples are given to verify the theoretical results and demonstrate an application to the design of associative memories. It is shown by an experimental example that delayed hybrid impulsive NNs have the advantages of high storage capacity and high fault tolerance when used for associative memories.

Reduced- and Full-Order Observers for Delayed Genetic Regulatory Networks

This paper is centered upon the state estimation for delayed genetic regulatory networks. Our aim is at estimating the concentrations of mRNAs and proteins by designing reduced-order and full-order state observers based on available network outputs. We introduce a Lyapunov-Krasovskii functional including quadruplicate integrals, and estimate its derivative by employing the Wirtinger-type integral inequalities, reciprocal convex technique, and convex technique. From which, delay-dependent sufficient conditions, in the form of linear matrix inequalities (LMIs), are investigated to ensure that the resultant error system is asymptotically stable. One can verify these conditions by utilizing the MATLAB Toolboxes LMI or YALMIP. In addition, the gains of reduced-order and full-order observers are represented by the feasible solutions of the LMIs, and thereby, the concrete expressions of the desired reduced-order and full-order state observers are presented. Finally, the simulation results of a numerical example are demonstrated, which explains the validity of the proposed method.

Improved results on state feedback stabilization for a networked control system with additive time-varying delay components' controller

This paper investigates the problems of stability and stabilization for a networked control system (NCS) with additive time-varying delay components' controller. Firstly, stability of a NCS with additive time-varying delays is investigated. A novel approach with free parameters is proposed. By constructing a new Lyapunov-Krasovskii functional (LKF) with two free parameters, stability criteria are obtained. The obtained stability criteria depend not only on upper bounds of delays but also free parameters. In addition, input-output method is extended to study the stability problem for the NCS. Compared with other approaches such as input-output method, the free-parameter approach is more flexible and effective in reducing the conservatism. Then, based on the stability results, a state feedback controller is designed to guarantee the asymptotically stable of the closed-loop systems. Finally, numerical examples are provided to show the effectiveness and less conservatism of the proposed results.

Synchronization of Reaction-Diffusion Neural Networks With Dirichlet Boundary Conditions and Infinite Delays

This paper is concerned with synchronization for a class of reaction-diffusion neural networks with Dirichlet boundary conditions and infinite discrete time-varying delays. By utilizing theories of partial differential equations, Green's formula, inequality techniques, and the concept of comparison, algebraic criteria are presented to guarantee master-slave synchronization of the underlying reaction-diffusion neural networks via a designed controller. Additionally, sufficient conditions on exponential synchronization of reaction-diffusion neural networks with finite time-varying delays are established. The proposed criteria herein enhance and generalize some published ones. Three numerical examples are presented to substantiate the validity and merits of the obtained theoretical results.

Further triple integral approach to mixed-delay-dependent stability of time-delay neutral systems

This paper studies the asymptotic stability for a class of neutral systems with mixed time-varying delays. Through utilizing some Wirtinger-based integral inequalities and extending the convex combination technique, the upper bound on derivative of Lyapunov-Krasovskii (L-K) functional can be estimated more tightly and three mixed-delay-dependent criteria are proposed in terms of linear matrix inequalities (LMIs), in which the nonlinearity and parameter uncertainties are also involved, respectively. Different from those existent works, based on the interconnected relationship between neutral delay and state one, some novel triple integral functional terms are constructed and the conservatism can be effectively reduced. Finally, two numerical examples are given to show the benefits of the proposed criteria.