Analysis on delay-dependent stability for neural networks with time-varying delays

Some Novel Results on Stability Analysis of Generalized Neural Networks With Time-Varying Delays via Augmented Approach

This article proposes three new methods to enlarge the feasible region for guaranteeing stability for generalized neural networks having time-varying delays based on the Lyapunov method. First, two new zero equalities in which three states are augmented are proposed and inserted into the results of the time derivative of the constructed Lyapunov-Krasovskii functionals for the first time. Second, inspired by the Wirtinger-based integral inequality, new Lyapunov-Krasovskii functionals are introduced. Finally, by utilizing the relationship among the augmented vectors and from the original equation, newly augmented zero equalities are established and Finsler's lemma are applied. Through three numerical examples, it is verified that the proposed methods can contribute to enhance the allowable region of maximum delay bounds.

Stability and dissipativity criteria for neural networks with time-varying delays via an augmented zero equality approach

This work investigates the stability and dissipativity problems for neural networks with time-varying delay. By the construction of new augmented Lyapunov-Krasovskii functionals based on integral inequality and the use of zero equality approach, three improved results are proposed in the forms of linear matrix inequalities. And, based on the stability results, the dissipativity analysis for NNs with time-varying delays was investigated. Through some numerical examples, the superiority and effectiveness of the proposed results are shown by comparing the existing works.

New Results on Stability Analysis for Delayed Markovian Generalized Neural Networks With Partly Unknown Transition Rates

The stability of delayed Markovian generalized neural networks is studied where the transition rates of the modes are partly unknown. The partly unknown transition rates generalize the traditional works that are with all known transition rates. Then, a Lyapunov-Krasovskii functional (LKF) with a delay-product-type (DPT) term is constructed. The DPT term is not only simple but also fully utilizes the information of time delay. Based on the new DPT LKF, stability criteria are presented, which are with lower computational complexity and less conservative. In the end, the validity and superiorities of the analytical results are verified by several examples.

Reduced-Order Filtering of Delayed Static Neural Networks With Markovian Jumping Parameters

The reduced-order filtering problems are investigated in this paper for static neural networks with Markovian jumping parameters and mode-dependent time-varying delays. By fully making use of integral inequalities, the designs of reduced-order and filters are discussed. The proper gain matrices of filters and the optimal performance indices are efficiently obtained by resolving corresponding convex optimization problems with the constraints of linear matrix inequalities. It is verified that the computational complexity for the reduced-order filter design is significantly reduced when compared with the full-order one. Furthermore, the nonfragile reduced-order filtering problems are also resolved in this paper. Two examples with simulation results are presented to demonstrate the feasibility and application of the established results.

Improved Stability Criterion for Recurrent Neural Networks With Time-Varying Delays

In this brief, the problem of delay-dependent stability of recurrent neural networks with time-varying delays is studied. A newly augmented Lyapunov-Krasovskii functional (LKF) that considers the information of the nonzero lower bound of time-varying delays is developed. Moreover, the information of the delayed state terms is not considered as elements of augmented vectors when constructing the LKF. An improved stability criterion with the framework of linear matrix inequalities is derived by employing the integral inequality and reciprocally convex combination. With the comparison to the existing ones, the developed stability criterion for neural networks has less conservatism and complexity. Finally, two widely used numerical examples are given to show the effectiveness and superiority of the obtained stability criterion.

Stability Analysis of Neural Networks With Time-Varying Delay by Constructing Novel Lyapunov Functionals

This paper presents two novel Lyapunov functionals for analyzing the stability of neural networks with time-varying delay. Based on our newly proposed Lyapunov functionals and a relaxed Wirtinger-based integral inequality, new stability criteria are derived in the form of linear matrix inequalities. A comprehensive comparison of results is given to illustrate the newly proposed stability criteria from both the conservative and computational complexity point of views.

Delay-dependent finite-time boundedness of a class of Markovian switching neural networks with time-varying delays

In this paper, a novel method is developed for delay-dependent finite-time boundedness of a class of Markovian switching neural networks with time-varying delays. New sufficient condition for stochastic boundness of Markovian jumping neural networks is presented and proved by an newly augmented stochastic Lyapunov-Krasovskii functional and novel activation function conditions, the state trajectory remains in a bounded region of the state space over a given finite-time interval. Finally, a numerical example is given to illustrate the efficiency and less conservative of the proposed method.