直接调节系统的一个绝对稳定准则

A Criterion of Absolute Stability of Direct Regulated System

本文应用直接方法研究直接调节系统的绝对稳定性问题.提出一种处理“二次型加非线性函数的积分”形式的函数的方法,并得到一个新的绝对稳定准则.这个准则表明,有名的Popoy准则当其中的参数取无穷值时,只要加上适当的条件,也可以保证系统的绝对稳定性.

In this article, the problem of absolute stability of direct regulated system:is disscused by Liapunov's direct method. A method of construction of Liapu-nov function is given. This Liapunov function has form of x plus an integral of a nonlinear function (?)(σ), that isthe derivative of V along the system (1) is a negative indefinite quadratic form of variables x and (?).We get the following results:Theorem 1. Assume that the matrix A is stable, the vectors a, b satisfy the following two inequalitiesand for real number ω,then the system (1) is absolutely stable in angle [0,μ0](μ0<∝).Theorem 2. Assume that the matrix A is stable, and vectors a , b satisfy the inequalityb*a<0 and for real number ωthen the system (1) is absolutely stable.