基于逻辑选择脉冲时滞动力系统的稳定性分析

Stability Analysis of Time-delayed Dynamic Systems with Impulsive Effects due to Logical Selection

为了使动力系统在稳定性分析上更具有一般化,能更加精确实际地刻画自然现象;针对具有逻辑选择脉冲效应的时滞动力系统,提出此系统的全局指数稳定性分析问题,可在一定程度上推广一般脉冲时滞动力系统的稳定性分析;通过引入具有逻辑选择脉冲效应的时滞非线性动力系统,并利用半张量积将该动力系统中的逻辑函数转换为代数状态空间表示,再建立脉冲型Halanay微分不等式来估计该动力系统中线性系统部分的Cauchy矩阵;基于此,对向量和函数给出了4个假设条件,得到在逻辑选择脉冲控制下的非线性时滞系统的零解全局指数稳定性判定依据,且证明了此动力系统的指数收敛率为λ-η。

In order to make the stability analysis of dynamic systems more general and to portray natural phenomena more accurately and practically,the stability analysis of the global exponential was proposed for a time-delay dynamic system with a logical selection impulse effect.The stability analysis of general impulse time-delayed dynamic systems can be extended to a certain extent.By introducing a time-delayed nonlinear dynamic system with logically selected impulsive effects,the logistic functions in this dynamic system were converted into an algebraic state space representation using the half-tensor product.An impulsive Halanay differential inequality was then developed to estimate the Cauchy matrix of the linear part of the dynamic system.Based on this,four assumptions were given for the vectors and functions,and a basis for determining the global exponential stability of the zero solution of a nonlinear time-delayed system under the control of a logically selected pulse was obtained.The exponential convergence rate of this dynamic system was proved to beλ-η.