具滞后的离散广义双线性系统的稳定控制分析

Stable Controlling Analysis for Discrete Singular Bilinear Systems with Time-delay

针对两类不同形式的滞后离散广义双线性系统的稳定控制问题进行了讨论.首先通过构造广义Lyapunov函数的方法,对其中一类形式的闭环系统稳定性问题进行分析,给出了系统零解E-渐近稳定的充分条件.在此条件基础上,利用等价变换和等价系统的方法,得到了该闭环系统Lyapunov意义下渐近稳定的充分条件.然后,研究了另一形式的滞后离散广义双线性系统稳定控制存在的条件,并给出了使闭环系统局部渐近稳定的充分条件.

In this paper, the stability problems of two forms about the discrete singular bilinear system with time——delay are investigated. Firstly, analysis on the problem of stability for the closed loop system in one forn of the above system is presented by constructing singular Lyapunov function, a sufficient condition on E--asymptotic stability of the system is given. Based on it, another sufficient condition on asymptotic stability undering the meaning of Lyapunov＇ s is obtained via the method of equivalent transformation and equivalent system. Furthermore, the existing condition of stable controlling for another form of the system is studied and the sufficient condition of making a closed loop system asymptotically stable in local bound is also discussed.