Mixed Time Delays Research Articles

Multiple periodic solutions of delayed competitive neural networks via functional differential inclusions

In this paper, a class of general competitive neural networks with discontinuous right-hand sides and mixed time delays is investigated. Based on functional differential inclusions theory and fixed point theorem of set-valued maps, the existence of one and multiple positive periodic solutions for the competitive neural networks are obtained. Without assuming the boundedness or satisfying a growth condition of discontinuous neuron activation functions, the results on the existence of one and multiple positive periodic solutions will also be valid. Some numerical examples are given to show the applicability and effectiveness of our main results.

Projective lag synchronization of Markovian jumping neural networks with mode-dependent mixed time-delays based on an integral sliding mode controller

In this paper, the mode-dependent projective synchronization problem of stochastic neural networks with mixed time-delays is investigated. By considering a proper sliding model surface, a sliding mode controller (SMC) is synthesized to guarantee the reach-ability of the specified sliding surface. The globally asymptotically stable of the sliding mode dynamical system is surveyed with the Lyapunov stability theory and linear matrix inequality (LMI) technique. A sufficient projective synchronization criterion for the stochastic neural networks is derived. Finally, numerical simulations are exploited to illustrate the effectiveness of the main results.

Adaptive anti-synchronization and [formula omitted] anti-synchronization for memristive neural networks with mixed time delays and reaction–diffusion terms

This paper firstly treats of the anti-synchronization of a class of memristor-based neural networks with mixed time delays and reaction–diffusion terms. An adaptive controller is designed such that the response system can be synchronized with the drive system by utilizing Lyapunov stability theory. Furthermore, the synchronization criteria derived in this paper are associated with the time switching. In addition, the H∞ anti-synchronization of memristive neural networks has been studied as well. Therefore, the results obtained in this paper are more general and extend the previous work. Finally, two numerical examples and their simulations are given to show the effectiveness of the obtained results.

Globally exponential stabilization of neural networks with mixed time delays via impulsive control

The impulsive stabilization problem of neural networks with discrete time-varying delays and unbounded continuously distributed delays is considered. By using impulse-time-dependent Lyapunov function-based techniques to capture the hybrid structure characteristics of the considered impulsive neural networks, two novel global exponential stability criteria are obtained in terms of linear matrix inequalities, which are capable of dealing with the case where both the continuous and discrete dynamics are unstable. When the original continuous-time delayed neural networks are not stable, sufficient conditions are developed for the design of exponentially stable linear impulsive state feedback controllers. Four numerical examples are given to illustrate the less conservatism and effectiveness of the proposed results.

Synchronization of continuous-time Markovian jumping singular complex networks with mixed mode-dependent time delays

In this paper, the problem of globally synchronization is investigated for an array of N linearly coupled singular complex networks with Markovian jump and mixed time-delays. The complex network systems consist of m modes and the systems switch from one mode to another according to a Markovian chain with known transition probability. The time delays include discrete delays and distributed delays. The singular matrices in the consider systems are mode-dependent. By utilizing the Lyapunov–Krasovskii stability theory, linear matrix inequality (LMI) approach, stochastic analysis techniques and Kronecker product, some sufficient globally synchronization criteria are obtained. Several numerical examples are given to illustrate the feasibility and effectiveness of the proposed methods.

Event-Triggered State Estimation for Complex Networks With Mixed Time Delays via Sampled Data Information: The Continuous-Time Case.

In this paper, the event-triggered state estimation problem is investigated for a class of complex networks with mixed time delays using sampled data information. A novel state estimator is presented to estimate the network states. A new event-triggered transmission scheme is proposed to reduce unnecessary network traffic between the sensors and the estimator, where the sampled data is transmitted to the estimator only when the so-called "event-triggered condition" is satisfied. The purpose of the problem addressed is to design an estimator for the complex network such that the estimation error is ultimately bounded in mean square. By utilizing Lyapunov theory combined with the stochastic analysis approach, sufficient conditions are established to guarantee the ultimate boundedness of the estimation error in mean square. Then, the desired estimator gain matrices are obtained via solving a convex problem. Finally, a numerical example is given to illustrate the effectiveness of the results.

Almost Automorphic Solutions for Fuzzy Cohen-Grossberg Neural Networks with Mixed Time Delays

This paper is concerned with the problem of almost automorphic solutions of a class of fuzzy Cohen-Grossberg neural networks with mixed time delays and variable coefficients. Based on inequality analysis techniques and combining the exponential dichotomy with fixed point theorem, some sufficient conditions for the existence and global exponential stability of almost automorphic solutions are obtained. Finally, a numerical example is given to show the feasibility of our results.

Stability and Bifurcation Analysis of Cyclic Genetic Regulatory Networks with Mixed Time Delays

This paper analyzes the stability and bifurcation criteria of cyclic genetic regulatory networks with mixed time delays (discrete and Gamma-type distributed delays). It is of more realistic biological background to use Gamma-type distributed delay kernels to describe the delays in the process between genes. The key aim of our research is to reveal more about the dynamic functions played by biochemical parameters and different mechanisms of discrete and distributed time delays. The existence of positive equilibria in this kind of genetic network is verified. With the mathematical tools of subharmonic function and complex theory, exact conditions of biochemical parameters for stability and bifurcations in cyclic genetic regulatory networks with both positive and negative gains are deduced, respectively. Finally, several simulation examples are adopted to deepen our analysis.

Robust Stabilization andH∞Control for Uncertain Neural Networks with Mixed Time Delays

This paper is concerned with the problem of robust stabilization andH∞control for a class of uncertain neural networks. For the robust stabilization problem, sufficient conditions are derived based on the quadratic convex combination property together with Lyapunov stability theory. The feedback controller we design ensures the robust stability of uncertain neural networks with mixed time delays. We further design a robustH∞controller which guarantees the robust stability of the uncertain neural networks with a givenH∞performance level. The delay-dependent criteria are derived in terms of LMI (linear matrix inequality). Finally, numerical examples are provided to show the effectiveness of the obtained results.

Fractional time delay estimation algorithm based on the maximum correntropy criterion and the Lagrange FDF

In this paper, a novel algorithm for fractional time delay estimation is proposed. It is based on the maximum correntropy criterion and the Lagrange fractional delay filter (FDF). The instantaneous correntropy is introduced to measure the similarity between received signals and estimated ones in the proposed algorithm. It leads to an effective performance under both Gaussian and impulsive noises. The performances, including the convergence of the algorithm and the variance of the time delay estimation, are theoretically analyzed. Simulations demonstrate that the time delay estimation precision of the proposed algorithm is higher than that utilizing the mixed modulated Lagrange explicit time delay estimation (MMLETDE) especially under low generalized signal-to-noise ratio (GSNR).

Global stability analysis of competitive neural networks with mixed time-varying delays and discontinuous neuron activations

In this paper, the global stability has been investigated for a novel class of competitive neural networks with mixed time delays and discontinuous activations. Without presuming the boundedness of activation functions, we draw two set of sufficient conditions ensuring the existence, uniqueness of the equilibrium, global exponential asymptotic stability of the solution and the associated output of the solution converging to the output equilibrium point in measure, by linear matrix inequality, M-matrix, Leray–Schauder alternative theorem in multivalued analysis, general Lyapunov method, topological degree theory of set-valued map. Meanwhile, we present a result on the global convergence in finite time of given neural networks. The results in the literature are generalized and significantly improved. Finally, one example and simulations are presented to demonstrate the effectiveness of the theoretical results.

H∞ filtering for two-dimensional systems with mixed time delays, randomly occurring saturations and nonlinearities

This paper is concerned with the filtering problem for the two-dimensional (2-D) systems with mixed time delays which comprise both the discrete time-varying delays and the discrete distributed delays in states. Randomly occurring nonlinearities (RONs) and randomly occurring saturations (ROSs) are also considered, respectively, in the state-space model and the measurement output equation to reflect the nonlinear disturbance appearing in a random way and the limited communication capabilities of the sensors. The aim of this paper is focused on the design of a full-order filter such that the performance is guaranteed in the simultaneous presence of the mixed tim delays, RONs and ROSs. By utilizing the Kronecker product and the inequality technique, an energy-like function is developed to establish some sufficient criteria under which the filtering error system satisfies the prescribed disturbance attenuation performance. Furthermore, explicit expression of the filter parameters is also characterized. Numerical example provided in the end of the paper further demonstrates the effectiveness of the proposed design scheme.

The stability of impulsive stochastic Cohen-Grossberg neural networks with mixed delays and reaction-diffusion terms.

The global asymptotic stability of impulsive stochastic Cohen-Grossberg neural networks with mixed delays and reaction-diffusion terms is investigated. Under some suitable assumptions and using Lyapunov-Krasovskii functional method, we apply the linear matrix inequality technique to propose some new sufficient conditions for the global asymptotic stability of the addressed model in the stochastic sense. The mixed time delays comprise both the time-varying and continuously distributed delays. The effectiveness of the theoretical result is illustrated by a numerical example.

Robust stability analysis of uncertain genetic regulatory networks with mixed time delays

This study is concerned with the robust stability problem of uncertain genetic regulatory networks (GRNs) with random discrete time delays and distributed time delays which exist both in translation process and feedback regulation process. By utilizing a novel Lyapunov–Krasovskii functional which contains some triple integral terms and takes into account the ranges of delays, we derive sufficient delay-dependent conditions to ensure the asymptotically stability of GRNs with mixed time delays. Moreover, based on the idea of “delay decomposing”, “reciprocally convex combination approach”, less conservative conditions are obtained by using the lower bound lemma together with Jensen inequality. In addition, two corollaries are also been presented. Finally, numerical examples are presented to show the effectiveness of our proposed methods.

Mean-square exponential stability for stochastic discrete-time recurrent neural networks with mixed time delays

In this paper, the mean-square exponential stability problem for discrete-time recurrent neural networks with time-varying discrete and distributed delays is investigated. Considering the delay distributions, a novel class of Lyapunov functional is introduced. By exploiting all possible information in mixed time delays, a sufficient condition for the whole system to be mean-square exponentially stable is given. Numerical examples are proposed to illustrate the effectiveness of the method, and show that by using the approach in this paper, the obtained results are less conservative than the existing ones.

New results of stability analysis for a class of neutral-type neural network with mixed time delays

In this paper, by using Lyapunov–Krasovskii functionals involving triple terms, we investigate the global exponential robust stability for uncertain neutral-type neutral networks with discrete and distributed delays. Several stability criteria are derived for the delayed neural networks in terms of LMIs. Some numerical examples are given to illustrate the applicability of the obtained results by using LMI control toolbox in MATLAB.

Sampled-data state estimation for delayed neural networks with discontinuous activations

This paper firstly treats of the sampled-data state estimation issue for the dynamic neural networks with mixed time-delays and discontinuous activation. Based on the theory of differential inclusion and non-smooth analysis, several criteria are presented to guarantee the existence of the desired state sampled-data estimator for the discontinuous neural networks by solving some linear matrix equalities. The obtained results are also applicable to neural networks with continuous activations since they are a special cases of neural networks with discontinuous activations. Results of this paper improve a few previous known results. Finally, two numerical simulations are given to illustrate the effectiveness of the proposed methods.

Robust reliable H∞ control for stochastic neural networks with randomly occurring delays

Abstract This paper investigates the problem of robust stabilization for a class of discrete-time stochastic neural networks with randomly occurring discrete and distributed time-varying delays. More precisely, the neuron activation functions are assumed to be more general and satisfy sector-like nonlinearities. Moreover, the effects of both variation range and probability distribution of mixed time-delays are taken into consideration in the proposed problem. The main objective of this paper is to design a state feedback reliable H ∞ controller such that for all admissible uncertainties as well as actuator failure cases, the resulting closed-loop form of considered neural network is robustly asymptotically stable while satisfying a prescribed H ∞ performance constraint. Linear matrix inequality approach together with proper construction of Lyapunov–Krasovskii functional is employed for obtaining delay dependent sufficient conditions for the existence of robust reliable H ∞ controller. The obtained results are formulated in terms of linear matrix inequalities (LMIs) which can be easily solved by using the MATLAB LMI toolbox. Finally, a numerical example with simulation results is provided to illustrate the effectiveness of the obtained control law and less conservativeness of the proposed results.

A descriptor system approach to the delay-dependent exponential stability analysis for switched neutral systems with nonlinear perturbations

In this paper, the problem of exponential stability analysis for switched neutral systems with mixed time-delays and nonlinear perturbations based on descriptor system approach is addressed. Delay-dependent exponential stability results are derived in terms of linear matrix inequalities based on piecewise descriptor type Lyapunov–Krasovskii functional. Average dwell time approach is used to analyze switched neutral systems. In addition convex combination, delay decomposition and free-weighting matrix approaches have been employed to derive less conservative results. Further, numerical examples are illustrated to demonstrate the effectiveness and less conservativeness of the derived theoretical results.

Impulsive exponential synchronization of randomly coupled neural networks with Markovian jumping and mixed model-dependent time delays

In this paper, the exponential synchronization problem for an array of N randomly coupled neural networks with Markovian jump and mixed model-dependent time delays via impulsive control is investigated. The jump parameters are determined by a continuous-time, discrete-state Markovian chain, and the mixed time delays under consideration comprise both discrete and continuous distributed delays. By making use of the Kronecker product and some useful techniques, a novel Lyapunov–Krasovskii functional suitable for handling distributed delays was proposed and then we show that the addressed synchronization problem is solvable if a set of linear matrix inequalities (LMIs) are feasible. The results presented in this paper generalize and improve many known results. Two numerical examples are also given to show the effectiveness of the theoretical results.