Shanmugam Lakshmanan

Synchronization of memristor-based recurrent neural networks with two delay components based on second-order reciprocally convex approach

We extend the notion of Synchronization of memristor-based recurrent neural networks with two delay components based on second-order reciprocally convex approach. Some sufficient conditions are obtained to guarantee the synchronization of the memristor-based recurrent neural networks via delay-dependent output feedback controller in terms of linear matrix inequalities (LMIs). The activation functions are assumed to be of further common descriptions, which take a broad view and recover many of those existing methods. A Lyapunov-Krasovskii functional (LKF) with triple-integral terms is addressed in this paper to condense conservatism in the synchronization of systems with additive time-varying delays. Jensens inequality is applied in partitioning the double integral terms in the derivation of LMIs and then a new kind of linear combination of positive functions weighted by the inverses of squared convex parameters has emerged. Meanwhile, this paper puts forward a well-organized method to manipulate such a combination by extending the lower bound lemma. The obtained conditions not only have less conservatism but also less decision variables than existing results. Finally, numerical results and its simulations are given to show the effectiveness of the proposed memristor-based synchronization control scheme.

Stability criteria for BAM neural networks with leakage delays and probabilistic time-varying delays

This paper is concerned with the stability criteria for bidirectional associative memory (BAM) neural networks with leakage time delay and probabilistic time-varying delays. By establishing a stochastic variable with Bernoulli distribution, the information of probabilistic time-varying delay is transformed into the deterministic time-varying delay with stochastic parameters. Based on the Lyapunov-Krasovskii functional and stochastic analysis approach, delay-probability-distribution-dependent sufficient conditions are derived to achieve the globally asymptotically mean square stable of the considered BAM neural networks. The criteria are formulated in terms of a set of linear matrix inequalities (LMIs), which can be checked efficiently by use of some standard numerical packages. Finally, a numerical example and its simulations are given to demonstrate the usefulness and effectiveness of the proposed results.

A delay partitioning approach to delay-dependent stability analysis for neutral type neural networks with discrete and distributed delays

This paper is concerned with the stability analysis of neutral type neural networks with discrete and distributed delays. Some improved delay-dependent stability results are established by using a delay partitioning approach for the networks. By employing a new type of Lyapunov-Krasovskii functionals, new delay-dependent stability criteria are derived. All the criteria are expressed in terms of linear matrix inequalities (LMIs), which can be solved efficiently by using standard convex optimization algorithms. Finally, numerical examples are given to illustrate the less conservatism of the proposed method.

Design of state estimator for neural networks with leakage, discrete and distributed delays ☆

Abstract In this paper, the design problem of state estimator for neural networks with mixed time-varying delays and leakage delays has been investigated. By using appropriate model transformation that shifts the considered systems into the neutral-type time-delay systems, adapting a new Lyapunov–Krasovskii functional which takes into account the range of time-delay, and by making use of some inequality techniques, delay-dependent criteria are developed to estimate the neuron states through available output measurements such that the estimation error system is globally asymptotically stable. The criteria are formulated in terms of a set of linear matrix inequalities (LMIs), which can be checked efficiently by use of some standard numerical packages. Finally, three numerical examples and its simulations are given to demonstrate the usefulness and effectiveness of the presented results.

Delay-interval dependent robust stability criteria for stochastic neural networks with linear fractional uncertainties

In this paper, we study the delay-interval dependent robust stability criteria for stochastic neural networks with linear fractional uncertainties. The time-varying delay is assumed to belong to an interval and is a fast time-varying function. The uncertainty under consideration includes linear fractional norm-bounded uncertainty. Based on the new Lyapunov-Krasovskii functional, some inequality techniques and stochastic stability theory, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities. Finally, some numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI conditions.

Exponential synchronization of Markovian jumping neural networks with partly unknown transition probabilities via stochastic sampled-data control

This paper investigates the exponential synchronization for a class of delayed neural networks with Markovian jumping parameters and time varying delays. The considered transition probabilities are assumed to be partially unknown. In addition, the sampling period is assumed to be time-varying that switches between two different values in a random way with given probability. Several delay-dependent synchronization criteria have been derived to guarantee the exponential stability of the error systems and the master systems are stochastically synchronized with the slave systems. By introducing an improved Lyapunov-Krasovskii functional (LKF) including new triple integral terms, free-weighting matrices, partly unknown transition probabilities and combining both the convex combination technique and reciprocal convex technique, a delay-dependent exponential stability criteria is obtained in terms of linear matrix inequalities (LMIs). The information about the lower bound of the discrete time-varying delay is fully used in the LKF. Furthermore, the desired sampled-data synchronization controllers can be solved in terms of the solution to LMIs. Finally, numerical examples are provided to demonstrate the feasibility of the proposed estimation schemes from its gain matrices.

Exponential stability of Markovian jumping stochastic Cohen-Grossberg neural networks with mode-dependent probabilistic time-varying delays and impulses

This paper deals with robust exponential stability of Markovian jumping stochastic Cohen-Grossberg neural networks (MJSCGNNs) with mode-dependent probabilistic time-varying delays, continuously distributed delays and impulsive perturbations. By construction of novel Lyapunov-Krasovskii functional having the triple integral terms, the double integral terms having the positive definite matrices dependent on the system mode and MJSCGNNs system transformation variables, new delay-dependent exponential stability conditions are derived in terms of linear matrix inequalities (LMIs). By establishing a stochastic variable with Bernoulli distribution, the information of probabilistic time-varying delay is considered and transformed into one with deterministic time-varying delay and stochastic parameters. Furthermore, a mode-dependent mean square robust exponential stability criterion is derived by constriction of new Lyapunov-Krasovskii functional having modes in the integral terms, linear matrix inequalities and some stochastic analysis techniques. Finally, two numerical examples are provided to show the effectiveness of the proposed methods.

Design of state estimator for genetic regulatory networks with time-varying delays and randomly occurring uncertainties ☆

In this paper, the design problem of state estimator for genetic regulatory networks with time delays and randomly occurring uncertainties has been addressed by a delay decomposition approach. The norm-bounded uncertainties enter into the genetic regulatory networks (GRNs) in random ways, and such randomly occurring uncertainties (ROUs) obey certain mutually uncorrelated Bernoulli distributed white noise sequences. Under these circumstances, the state estimator is designed to estimate the true concentration of the mRNA and the protein of the uncertain GRNs. Delay-dependent stability criteria are obtained in terms of linear matrix inequalities by constructing a Lyapunov-Krasovskii functional and using some inequality techniques (LMIs). Then, the desired state estimator, which can ensure the estimation error dynamics to be globally asymptotically robustly stochastically stable, is designed from the solutions of LMIs. Finally, a numerical example is provided to demonstrate the feasibility of the proposed estimation schemes.

Effects of leakage time-varying delays in Markovian jump neural networks with impulse control

In this paper, the stability analysis problem is investigated for delayed neural networks with mixed time-varying delays, impulsive control and Markovian jumping parameters. The mixed time-varying delays include leakage, discrete and distributed time-varying delays. Sufficient conditions for the global exponential stability in the mean square are derived by using Lyapunov-Krasovskii functional having triple integral terms and model transformation technique. The stability criterion that depends on the upper bounds of the leakage time-varying delay and its derivative is given in terms of linear matrix inequalities (LMIs), which can be efficiently solved via standard numerical softwares. Finally, three numerical examples and simulations are given to demonstrate the usefulness and effectiveness of the presented results.

State Estimation for Genetic Regulatory Networks With Mode-Dependent Leakage Delays, Time-Varying Delays, and Markovian Jumping Parameters

This paper considers the state estimation problem for Markovian jumping genetic regulatory networks (GRNs) with mode-dependent leakage and time-varying delays. In order to approximate the true concentrations of the mRNA and protein, the state estimator is designed using available measurement outputs. The GRNs are composed of N modes. The system switches from one mode to another according to a Markovian chain with known transition probabilities. Based on the Lyapunov functionals, including triple integral terms, some inequalities, and a time-varying delay partitioning approach, delay-dependent criteria which employ all upper bounds of time delays of each mode are obtained in terms of linear matrix inequalities (LMIs). This guarantees that the estimation error dynamics can be globally asymptotically stable from solutions of LMIs. Finally, a numerical example is presented to demonstrate the efficiency of the proposed estimation scheme.