一种迟滞微分系统的稳定与控制问题研究

Research on the Problem of the Stability and Control of a Kind of Delay Differential System

基于李雅普诺夫两种方法,给出一种双曲函数型辅助方程及其相关结论;通过几个步骤,研究了一种迟滞微分系统的求解、稳定与控制问题.步骤一、给出双函数型辅助方程的精确解.步骤二、通过双曲函数变换与双曲函数型辅助方程,将一种迟滞微分系统的求解问题转化为非线性代数方程组的求解问题.步骤三、借助符号计算系统Mathematica求出代数方程组的解,并构造了一种迟滞微分系统的精确解.步骤四、用符号计算系统Mathematica研究迟滞微分系统的稳定与控制问题.

Two kinds of Lyapunov method are presented to put forward a kind of hyperbolic function type auxiliary equation and its relative conclusions. By some steps, the problems of solving the solution,stability and control of a kind of delay differential system are researched. Step 1, the accurate solutions of the hyperbolic function type auxiliary equation are presented. Step 2, by a hyperbolic function transformation and hyperbolic function type auxiliary equation, the problem of solving solutions of a kind of delay differential system is changed to the problem of solving solutions of the nonlinear algebra equations. Step 3,with the help of the symbol calculate system Mathematica,the solutions of the algebra equations are solved,and the accurate solutions of a kind of delay differential system are constructed. Step 4,with the help of the symbol calculate system Mathematica,the problem of the stability and control of a kind of delay differential system is researched.