非线性大系统在有限域中的鲁棒稳定性

本文研究了含有不确定参数的非线性大系统的稳定性,当参数向量受到限制时,这种稳定 性称为鲁棒(粗壮)稳定性.在状态空间的含原点的有限域中,利用李亚普诺夫函数进行集结 线性化,可将大系统化为线性系统,由于线性化的任意性,得到的线性系统不是唯一的.文 中阐明了利用图论方法建立的大系统的多层结构可以简化稳定性判据,帮助选择局部反馈,以 实现大系统的镇定.

Robust Stability in Finite Region of Large Scale Systems

The stability of nonlinear large scale systems containing contrained uncertain parameters is studied in this paper. This kind of stability is called robust stability when the vectors of the parameters are constrained. The large scale system can be reduced to a linear system by aggregation linearization via Liapunov functions in the finite region of the state space containing the origin. This linear system obtained is not unique due to the flexibility occuring in linearization. It is shown that the hierarchical structure of the large scale system estabilished by graph theoretic method can simplify the finite region stability criteria and help in choosing local feedbacks for stabilizing the large scale system.