Lyapunov function

Xem 1-20 trên 22 kết quả Lyapunov function
  • 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.

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  • Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: LYAPUNOV FUNCTIONS FOR LINEAR NONAUTONOMOUS DYNAMICAL EQUATIONS ON TIME SCALES

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  • 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.

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  • 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.

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  • A constructive method is presented to design bounded and continuous cooperative controllers that force a group of N mobile agents with limited sensing ranges to stabilize at a desired location, and guarantee no collisions between the agents. The control development is based on new general potential functions, which attain the minimum value when the desired formation is achieved, are equal to infinity when a collision occurs, and are continuous at switches. The multiple Lyapunov function (MLF) approach is used to analyze stability of the closed loop switched system.

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  • In this paper, sufficient criteria that guarantee the existence of stochastic asymptotic stability of the zero solution of the nonautonomous second-order stochastic delay differential equation were established with the aid of a suitable Lyapunov functional. Two examples are given in the last section to illustrate our main result.

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  • This is the main result of the paper. We use the method to estimate the region of attraction for the case of the asymptotical stability. We study this technique for the case autonomous systems.

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  • Abstract In this paper we demonstrate how Lyapunov-Krasovskii functionals can be used to obtain exponential bounds for the solutions of time-invariant linear delay systems. Keywords: time delay system, exponential estimate, Lyapunov-Krasovskii functional. The objective of this note is to describe a systematic procedure of constructing quadratic Lyapunov functionals for (exponentially) stable linear delay systems in order to obtain exponential estimates for their solutions.

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  • FUZZY DESCRIPTOR SYSTEMS AND CONTROL This chapter deals with a fuzzy descriptor system defined by extending the original Takagi-Sugeno fuzzy model. A number of stability conditions for the fuzzy descriptor system are derived and represented in terms of LMIs. A motivating example for using the fuzzy descriptor system instead of the original Takagi-Sugeno fuzzy model is presented. An LMI-based design approach is employed to find stabilizing feedback gains and a common Lyapunov function.

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  • Modern complex dynamical systems1 are highly interconnected and mutually interdependent, both physically and through a multitude of information and communication network constraints. The sheer size (i.e., dimensionality) and complexity of these large-scale dynamical systems often necessitates a hierarchical decentralized architecture for analyzing and controlling these systems. Specifically, in the analysis and control-system design of complex large-scale dynamical systems it is often desirable to treat the overall system as a collection of interconnected subsystems.

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  • T he impetus to produce this book came in a brief phone call in 1998. Chuck Crumly, of Academic Press, called with an invitation and a deadline. Either The Ecology of Fishes on Coral Reefs, published in 1991, would be allowed to lapse into out-of-print status, or I would agree to produce a second edition. Looking back on all the work, I suspect it might have been wiser to say, "Let her lapse." But I didn't.

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  • For bidirectional associate memory neural networks with time-varying delays, the problems of determining the exponential stability and estimating the exponential convergence rate are investigated by employing the Lyapunov functional method and linear matrix inequality (LMI) technique. A novel criterion for the stability, which give information on the delay-dependent property, is derived.

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  • 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.

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  • 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).

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  • This paper presents a method of using Sliding Mode Control (SMC) for Cart and Pole system. The stability of controller is proved through using Lyapunov function and simulations. A genetic algorithm (GA) program is used to optimize controlling parameters.

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  • This paper deals with the problem of asymptotic stability for a class of nonlinear discrete-time 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 constructing improved Lyapunov functionals, delay-depenent criteria for the asymptotic stability of the system are established via linear matrix inequalities. A numerical example is given to show the effectiveness of the result..

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  • The aim of this paper is to study the almost sure exponential stability of stochastic differential delay equations on time scales. This work can be considered as a unification and generalization of stochastic difference and stochastic differential delay equations.

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  • We study the long time behavior of the bounded solutions of non homogeneous gradient-like system which admits a strict Lyapunov function. More precisely, we show that any bounded solution of the gradient-like system converges to an accumulation point as time goes to infinity under some mild hypotheses.

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  • 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.

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  • 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.

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