关于稳定性问题的教学讨论——引入ISS稳定性概念的必要性

Argumentation on How to Teach Stability ——Requirement for Introducing Input-to-State Stability

对于工程系统,如果其输入作用是有界的,其状态变量也应是有界的;这正是我们为什么要在控制理论中引入输入状态稳定(ISS)概念的原因。在线性系统的稳定性分析中,我们往往只给出了内部稳定与外部稳定的概念,但对于线性时变系统而言,这两个概念也不足以保证系统稳定性的基本要求;因此在《线性系统理论》的教学中,引入ISS稳定性的概念是非常必要的。

For engineering system, if its inputs are bounded, its state variables must be bounded. This is the very reason why the concept of ISS is necessary in control theory . However, in the stability analysis of linear systems, only the concepts of the internal stability and external stability are given . But for linear time-varying systems, these two kind concepts of stability can't satisfy the basic requirement for system stability. In conclusion, it is very necessary to introduce the concept of ISS in the course of Linear System Theory .