New passivity results for uncertain discrete-time stochastic neural networks with mixed time delays

Improved Stability Criteria for Discrete-Time Delayed Neural Networks via Novel Lyapunov-Krasovskii Functionals

This article investigates the stability problem for discrete-time neural networks with a time-varying delay by focusing on developing new Lyapunov-Krasovskii (L-K) functionals. A novel L-K functional is deliberately tailored from two aspects: 1) the quadratic term and 2) the single-summation term. When the variation of the discrete-time delay is further considered, the constant matrix involved in the quadratic term is extended to be a delay-dependent one. All these innovations make a contribution to a quadratic function with respect to the delay from the forward differences of L-K functionals. Consequently, tractable stability criteria are derived that are shown to be more relaxed than existing results via numerical examples.

Partial-Neurons-Based Passivity-Guaranteed State Estimation for Neural Networks With Randomly Occurring Time Delays

In this brief, the partial-neurons-based passivity-guaranteed state estimation (SE) problem is examined for a class of discrete-time artificial neural networks with randomly occurring time delays. The measurement outputs available utilized for the SE are allowed to be available only at a fraction of neurons in the networks. A Bernoulli-distributed random variable is employed to characterize the random nature of the occurrence of time delays. By resorting to the Lyapunov-Krasovskii functional method as well as the stochastic analysis technique, sufficient criteria are provided for the existence of the desired state estimators ensuring the estimation error dynamics to achieve the asymptotic stability in the mean square with a guaranteed passivity performance level. In addition, the parameterization of the estimator gain is acquired by solving a convex optimization problem. Finally, the validity of the obtained theoretical results is illustrated via a numerical simulation example.

Stability Analysis of Discrete-Time Neural Networks With Time-Varying Delay via an Extended Reciprocally Convex Matrix Inequality

This paper is concerned with the stability analysis of discrete-time neural networks with a time-varying delay. Assessment of the effect of time delays on system stability requires suitable delay-dependent stability criteria. This paper aims to develop new stability criteria for reduction of conservatism without much increase of computational burden. An extended reciprocally convex matrix inequality is developed to replace the popular reciprocally convex combination lemma (RCCL). It has potential to reduce the conservatism of the RCCL-based criteria without introducing any extra decision variable due to its advantage of reduced estimation gap using the same decision variables. Moreover, a delay-product-type term is introduced for the first time into the Lyapunov function candidate such that a delay-variation-dependent stability criterion with the bounds of delay change rate is established. Finally, the advantages of the proposed criteria are demonstrated through two numerical examples.

Robust control of uncertain nonlinear switched genetic regulatory networks with time delays: A redesign approach

In this paper, the problem of robust stability of nonlinear genetic regulatory networks (GRNs) is investigated. The developed method is an integral sliding mode control based redesign for a class of perturbed dissipative switched GRNs with time delays. The control law is redesigned by modifying the dissipativity-based control law that was designed for the unperturbed GRNs with time delays. The switched GRNs are switched from one mode to another based on time, state, etc. Although, the active subsystem is known in any instance, but the switching law and the transition probabilities are not known. The model for each mode is considered affine with matched and unmatched perturbations. The redesigned control law forces the GRN to always remain on the sliding surface and the dissipativity is maintained from the initial time in the presence of the norm-bounded perturbations. The global stability of the perturbed GRNs is maintained if the unperturbed model is globally dissipative. The designed control law for the perturbed GRNs guarantees robust exponential or asymptotic stability of the closed-loop network depending on the type of stability of the unperturbed model. The results are applied to a nonlinear switched GRN, and its convergence to the origin is verified by simulation.

New Results on Passivity Analysis of Stochastic Neural Networks with Time-Varying Delay and Leakage Delay

The passivity problem for a class of stochastic neural networks systems (SNNs) with varying delay and leakage delay has been further studied in this paper. By constructing a more effective Lyapunov functional, employing the free-weighting matrix approach, and combining with integral inequality technic and stochastic analysis theory, the delay-dependent conditions have been proposed such that SNNs are asymptotically stable with guaranteed performance. The time-varying delay is divided into several subintervals and two adjustable parameters are introduced; more information about time delay is utilised and less conservative results have been obtained. Examples are provided to illustrate the less conservatism of the proposed method and simulations are given to show the impact of leakage delay on stability of SNNs.

Passivity and passification of memristor-based recurrent neural networks with time-varying delays

This paper presents new theoretical results on the passivity and passification of a class of memristor-based recurrent neural networks (MRNNs) with time-varying delays. The casual assumptions on the boundedness and Lipschitz continuity of neuronal activation functions are relaxed. By constructing appropriate Lyapunov-Krasovskii functionals and using the characteristic function technique, passivity conditions are cast in the form of linear matrix inequalities (LMIs), which can be checked numerically using an LMI toolbox. Based on these conditions, two procedures for designing passification controllers are proposed, which guarantee that MRNNs with time-varying delays are passive. Finally, two illustrative examples are presented to show the characteristics of the main results in detail.

Robust stochastic stability of discrete-time fuzzy Markovian jump neural networks

This paper focuses the issue of robust stochastic stability for a class of uncertain fuzzy Markovian jumping discrete-time neural networks (FMJDNNs) with various activation functions and mixed time delay. By employing the Lyapunov technique and linear matrix inequality (LMI) approach, a new set of delay-dependent sufficient conditions are established for the robust stochastic stability of uncertain FMJDNNs. More precisely, the parameter uncertainties are assumed to be time varying, unknown and norm bounded. The obtained stability conditions are established in terms of LMIs, which can be easily checked by using the efficient MATLAB-LMI toolbox. Finally, numerical examples with simulation result are provided to illustrate the effectiveness and less conservativeness of the obtained results.

Dissipativity analysis for discrete-time stochastic neural networks with time-varying delays

In this paper, the problem of dissipativity analysis is discussed for discrete-time stochastic neural networks with time-varying discrete and finite-distributed delays. The discretized Jensen inequality and lower bounds lemma are adopted to deal with the involved finite sum quadratic terms, and a sufficient condition is derived to ensure the considered neural networks to be globally asymptotically stable in the mean square and strictly (Q, S, R)-y-dissipative, which is delay-dependent in the sense that it depends on not only the discrete delay but also the finite-distributed delay. Based on the dissipativity criterion, some special cases are also discussed. Compared with the existing ones, the merit of the proposed results in this paper lies in their reduced conservatism and less decision variables. Three examples are given to illustrate the effectiveness and benefits of our theoretical results.

Exponential synchronization of neural networks with discrete and distributed delays under time-varying sampling

This paper investigates the problem of master-slave synchronization for neural networks with discrete and distributed delays under variable sampling with a known upper bound on the sampling intervals. An improved method is proposed, which captures the characteristic of sampled-data systems. Some delay-dependent criteria are derived to ensure the exponential stability of the error systems, and thus the master systems synchronize with the slave systems. The desired sampled-data controller can be achieved by solving a set of linear matrix inequalitys, which depend upon the maximum sampling interval and the decay rate. The obtained conditions not only have less conservatism but also have less decision variables than existing results. Simulation results are given to show the effectiveness and benefits of the proposed methods.