摘要
讨论了一类具有有界可变时滞分离变量系统平衡点的全局指数稳定性。在所给函数为Lipschitz连续的情况下,利用Lyapunov 函数方法并结合Halanay时滞微分不等式,分别构造适当的连续但不一定可微的数量或向量Lyapunov函数和二次型Lyapunov函数,获得了几个保证此类分离变量型时滞系统的平衡点为全局指数稳定的时滞相关和时滞无关的代数判据。这些判据将问题化为代数不等式或M矩阵,可以直接根据系统方程进行检验,便于实际应用。
The global exponential stability of equilibrium states of a class of nonlinear separated variables systems with bounded time-varying delays was investigated. Based on Lipschitz continuous functions and Lyapunov functions method and the Halanay's delay differential inequality, some algebraic criterions of globally exponential stability for the type of systems are obtained via constructing appropriate continuous and non-differential scalar and vector Lyapunov functions and quadratic form Lyapunov function, respectively, whose results are both independent of and dependent on the magnitudes of the delays. These criteria reduce the problem to a set of algebraic inequalities or M matrix and can be verified directly according to equation of the concerned systems, and therefore are convenient in practical use.
出处
《中南大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2005年第2期282-287,共6页
Journal of Central South University:Science and Technology
基金
国家自然科学基金资助项目(60274007
60474011)
教育部博士点基金资助项目(20010487005)
关键词
非线性时滞系统
全局指数稳定性
时滞微分不等式
分离变量
时变时滞
nonlinear delay system
global exponential stability
delay differential inequality
separated variables
time-varying delay
