输入状态稳定理论及其独立电力系统应用

Input-to-output stability theory and its application on isolated power system

对实际工程中的动态系统而言,Lyapunov稳定理论主要致力于分析在无外部信号激励的情况下,系统的状态能够从任意的初始点回到自身所固有的平衡状态的能力问题,由此导致其并不适合分析和处理系统存在持续扰动(包括有界的外部信号)激励下,系统的状态响应能否处于某一事先设定的有界范围的问题。有鉴于此,输入-状态稳定理论应运而生。该理论将Lyapunov方法与算子法相结合,系统地提出了ISS的概念、定义、模型和方法,其中局部ISS稳定自动分析方法及互联系统ISS小增益定理等进展为该理论在独立电力系统的实用化打下了理论基础。

For practical dynamic system, Lyapunov stability theory focuses on the ability of a system to go back to certain equilibrium from arbitrary initial point if there is no external input signal. Thus, Lyapunov theory is not suitable for analysis whether a system＇s state can be bounded by a pre-set region when the system has persistent disturbances （including bounded external signal）. For this reason, Input-to-State Stability （ISS） theory came into being. The theory unifies Lyapunov method and operator approach, and proposes the concept of ISS, definitions, models and methods systematically. Recent progresses, such as the automatic analysis method for local ISS and interconnection system＇s ISS small gain theorem, provide theoretical basis for ISS to be applied in isolated power systems.