The Lyapunov functional

In this paper, the problem of exponential stability for a class of nonlinear neutral systems with interval time-varying delay is studied. Based on improved Lyapunov-Krasovskii functionals combine with Leibniz-Newton’s formula, new delay-dependent sufficient conditions for the exponential stability of the systems are established in terms of linear matrix inequalities (LMIs), which allows to compute the maximal bound of the exponential stability rate of the solution.

11p tamynhan8 04-11-2020 15 2   Download

This paper addresses the problem of ℋ∞ finite-time boundedness for discrete-time neural networks with interval-like time-varying delays. First, a delay-dependent finite-time boundedness criterion under the finite-time ℋ ∞ performance index for the system is given based on constructing a set of adjusted Lyapunov–Krasovskii functionals and using reciprocally convex approach.

14p tamynhan6 14-09-2020 15 1   Download

Stroke is one of the main causes of disability. It affects millions of people worldwide. One symptom of stroke is disabled arm function. Restoration of arm function is necessary to resuming activities of daily living (ADL).

12p tohitohi 19-05-2020 15 1   Download

This paper deals with the problem of asymptotic stability for a class of switched nonlineardiscrete systems with time-varying delay. The time-varying delay is assumed to be belong to a given interval in which the lower bound of delay is not restricted to zero. A linear matrix inequality (LMI) approach to asymptotic stability of the system is presented. Based on the Lyapunov functional, delay-depenent criteria for the asymptotic stability of the system are established via linear matrix inequalities.

6p doctorstrange1 21-06-2018 32 2   Download

This paper addresses the synchronization of coupled chaotic Hindmarsh-Rose neurons. A sufficient condition for self-synchronization is first attained by using Lyapunov method. Also, to achieve the synchronization between two coupled Hindmarsh-Rose neurons when the selfsynchronization condition not satisfied, a Lyapunov-based nonlinear control law is proposed and its asymptotic stability is proved. To verify the effectiveness of the proposed method, numerical simulations are performed.

12p dieutringuyen 07-06-2017 23 2   Download

METHODS FOR DETERMINATION AND APPROXIMATION OF THE DOMAIN OF ATTRACTION IN THE CASE OF AUTONOMOUS DISCRETE DYNAMICAL SYSTEMS ST. BALINT, E. KASLIK, A. M. BALINT, AND A. GRIGIS Received 15 October 2004; Accepted 18 October 2004 A method for determination and two methods for approximation of the domain of attraction Da (0) of the asymptotically stable zero steady state of an autonomous, R-analytical, discrete dynamical system are presented. The method of determination is based on the construction of a Lyapunov function V , whose domain of analyticity is Da (0).

15p sting12 10-03-2012 47 5   Download

EXPONENTIAL STABILITY OF DYNAMIC EQUATIONS ON TIME SCALES ALLAN C. PETERSON AND YOUSSEF N. RAFFOUL Received 6 July 2004 and in revised form 16 December 2004 We investigate the exponential stability of the zero solution to a system of dynamic equations on time scales. We do this by defining appropriate Lyapunov-type functions and then formulate certain inequalities on these functions. Several examples are given. 1. Introduction This paper considers the exponential stability of the zero solution of the first-order vector dynamic equation x∆ = f (t,x), t ≥ 0. (1.

12p sting12 10-03-2012 44 5   Download

EXISTENCE AND GLOBAL STABILITY OF POSITIVE PERIODIC SOLUTIONS OF A DISCRETE PREDATOR-PREY SYSTEM WITH DELAYS LIN-LIN WANG, WAN-TONG LI, AND PEI-HAO ZHAO Received 13 January 2004 We study the existence and global stability of positive periodic solutions of a periodic discrete predator-prey system with delay and Holling type III functional response. By using the continuation theorem of coincidence degree theory and the method of Lyapunov functional, some sufficient conditions are obtained. 1.

16p sting12 10-03-2012 58 5   Download

LYAPUNOV FUNCTIONALS CONSTRUCTION FOR STOCHASTIC DIFFERENCE SECOND-KIND VOLTERRA EQUATIONS WITH CONTINUOUS TIME LEONID SHAIKHET Received 4 August 2003 The general method of Lyapunov functionals construction which was developed during the last decade for stability investigation of stochastic differential equations with aftereffect and stochastic difference equations is considered. It is shown that after some modification of the basic Lyapunov-type theorem, this method can be successfully used also for stochastic difference Volterra equations with continuous time usable in mathematical models.

25p sting12 10-03-2012 46 7   Download

Stability Issues in RNN Architectures Perspective The focus of this chapter is on stability and convergence of relaxation realised through NARMA recurrent neural networks. Unlike other commonly used approaches, which mostly exploit Lyapunov stability theory, the main mathematical tool employed in this analysis is the contraction mapping theorem (CMT), together with the fixed point iteration (FPI) technique. This enables derivation of the asymptotic stability (AS) and global asymptotic stability (GAS) criteria for neural relaxive systems.

19p doroxon 12-08-2010 104 9   Download