扩展的小增益定理

把接受瞬时信号的系统成立的结论推广到接受持久信号的系统,一直是鲁棒控制的基本问题,也是一个难题。在接受持久信号的系统中,很多原有的接受瞬时信号系统成立的结论都不成立了,因此大量的概念、定理需要改进。目前虽然对于一般的H∞函数和H∞不确定性模型来说,定义频域的概念已取得了一些成果,但是对于小增益定理的改进还是很少。基于此,应用H-∞1函数空间修改了小增益定理,给出了一个扩展的小增益定理。并且讨论了它的应用价值。

Developed Small Gain Theorem

It is a basic and difficult problem in control that extending the conclusions of accepted transient signal systems to persistent signal systems.In persistent signal systems,the results of accepted transient signal systems are not true.So a lot of definitions and theorems need to be modified.At present,for the general H_∞ functions and H_∞ uncertainty models,though some achievements in the definition of frequency concepts have been gained,it is little for modifying Small Gain Theorem.Therefore,we modify Small Gain Theorem in H~(-1)_∞ space and get a developed Small Gain Theorem,then we discuss the application value of it.