时滞离散广义大系统的稳定性分析与镇定

广义系统的渐近稳定与镇定问题是广义系统理论的基本问题之一,在许多领域均有广泛的应用.笔者从时滞离散广义大系统的满足容许的条件出发,利用Lyapunov方法,通过对输入矩阵加上范数有界的约束条件,分别对时滞离散广义大系统的线性情形和非线性情形的稳定性进行了分析,并结合矩阵的特征值分别给出了两种情形的渐近稳定性的判据.此外,在所有子系统都是正则的且具有因果关系的条件下,利用Lyapunov函数方法设计了适当的反馈律,以实现线性时滞离散广义大系统的镇定.该方法简单,直观,给出的数值例子说明判据的可行性和有效性.

Stability analysis and stabilization of discrete singular large-scale systems with time-delay

The problem of asymptotic stability and stabilization is one of the fundamental problems in singular system theory, and is used in many fields. Under the condition that all the isolated sub-sys- tems are admissible and the interconnecting matrices, input matrices and nonlinear parts are bounded in terms of matrix spectrum, the problem of stability of linear and nonlinear discrete singular large- scale systems with time-delay is investigated by the Lyapunov method. The criteria are presented in terms of eigenvalue of matrix to determine whether the discrete singular large-scale systems with time- delay are stable. Besides, under the condition that all isolated subsystems are regular and causal, the controller is designed for the stabilization of the linear discrete singular large-scale system with timedelay. The utilized method is simple, intuitional and easily understood. A numerical example is given to show the feasibility and effectiveness of the theorem.