Improved delay-dependent stability criterion for neural networks with time-varying delay

In this paper, the problem of delay-dependent asymptotic stability criterion for neural networks with time-varying delay has been considered. A new class of Lyapunov functional which contains a triple-integral term is constructed to derive some new delay-dependent stability criteria. The obtained criteria are less conservative because free-weighting matrices method and a convex optimization approach are considered. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.     

Stability of random impulsive coupled systems on networks with Markovian switching

Abstract

This article is intended to study global asymptotical stability in probability for random impulsive coupled systems on networks with Markovian switching. Two cases are considered. (1) Continuous dynamics are stable while impulses are unstable; (2) impulses are stable while continuous dynamics are unstable. To begin with, based on Lyapunov method as well as graph-theoretic technique, several new stability criteria in two cases are derived, that are, the Lyapunov-type criteria and the coefficients-type criteria. Then main results are used for a class of random impulsive coupled oscillators. Finally, the effectiveness of the obtained results is verified by numerical simulations.     

New delay-dependent robust stability criterion for uncertain neutral systems with time-varying delay and nonlinear uncertainties

This paper investigates the robust stability of uncertain neutral system with time-varying delay and nonlinear uncertainties. By using Lyapunov method and linear matrix inequality technology, a new delay-dependent stability criteria is obtained and formulated in terms of linear matrix inequalities (LMIs) which can be easy to check the robust stability of the considered systems. Numerical examples are given to indicate significant improvements over some existing results.     

Linear Matrix Inequality Approach to New Delay-Dependent Stability Criteria for Uncertain Dynamic Systems with Time-Varying Delays

In this paper, the problem of delay-dependent stability for uncertain dynamic systems with time-varying delays is considered. The parameter uncertainties are assumed to be norm-bounded. Using a new augmented Lyapunov functional, novel delay-dependent stability criteria for such systems are established in terms of LMIs (linear matrix inequalities), which can be solved easily by the application of convex optimization algorithms. Three numerical examples are given to show the superiority of the proposed method.     

一般Lurie系统的鲁棒绝对稳定新准则(英文)

本文讨论了具多非线性模不确定的一般Lurie系统的鲁棒问题.用Lyapunov函数方法,得到了一些新的鲁棒绝对稳定代数准则,这些准则减少了现有的结果的保守性.     

Exponential stability analysis for uncertain neural networks with interval time-varying delays

In this paper, the problem of exponential stability analysis for neural networks is investigated. It is assumed that the considered neural networks have norm-bounded parametric uncertainties and interval time-varying delays. By constructing a new Lyapunov functional, new delay-dependent exponential stability criteria with an exponential convergence rate are established in terms of LMIs (linear matrix inequalities) which can be easily solved by various convex optimization algorithms. Two numerical examples are included to show the effectiveness of proposed criteria.     

Extended VIKOR method in comparison with outranking methods

The VIKOR method was developed to solve MCDM problems with conflicting and noncommensurable (different units) criteria, assuming that compromising is acceptable for conflict resolution, the decision maker wants a solution that is the closest to the ideal, and the alternatives are evaluated according to all established criteria. This method focuses on ranking and selecting from a set of alternatives in the presence of conflicting criteria, and on proposing compromise solution (one or more). The VIKOR method is extended with a stability analysis determining the weight stability intervals and with trade-offs analysis. The extended VIKOR method is compared with three multicriteria decision making methods: TOPSIS, PROMETHEE, and ELECTRE. A numerical example illustrates an application of the VIKOR method, and the results by all four considered methods are compared.     

New results on global asymptotic stability analysis for neural networks with time-varying delays

This note provides new results on global asymptotic stability for neural networks with time-varying delay. Two types of time-varying delay are considered: one is differentiable and has bounded derivative; the other one is continuous and may vary very fast. By introducing an augmented Lyapunov–Krasovskii functional, new delay-dependent stability criteria for delayed neural networks are derived in terms of linear matrix inequalities (LMIs). It is shown that the obtained criteria can provide less conservative results than some existing ones. Numerical examples are given to demonstrate the applicability of the proposed approach.     

On the mean square stability of linear difference equations

The mean square asymptotic stability of linear stochastic difference equations is studied. The Liapunov method of stability analysis is extended to stochastic difference equations, and several criteria for the mean square stability of the equilibrium state are established. Two examples of the application of the stability theorems are also considered.     

Synchronization stability of general complex dynamical networks with time-varying delays: A piecewise analysis method

The synchronization problem of some general complex dynamical networks with time-varying delays is investigated. Both time-varying delays in the network couplings and time-varying delays in the dynamical nodes are considered. The delays considered in this paper are assumed to vary in an interval, where the lower and upper bounds are known. Based on a piecewise analysis method, the variation interval of the time delay is firstly divided into several subintervals, by checking the variation of the derivative of a Lyapunov function in every subinterval, then the convexity of matrix function method and the free weighting matrix method are fully used in this paper. Some new delay-dependent synchronization stability criteria are derived in the form of linear matrix inequalities. Two numerical examples show that our method can lead to much less conservative results than those in the existing references.