A local theory of input/output stability of dynamical systems

✍ Scribed by Horacio Marquez

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 677 KB
• Volume: 332
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(95)00035-v

✦ Synopsis

The purpose of this paper is to present a local theory of input/output stability OJ dynamical systems. More precisely, the intention is to obtain local open loop conditions for local closed loop stability of feedback interconnections. It will be shown that, by setting the problem in the context of extended binormed spaces it is possible to obtain local versions of the so-called small 9ain theorem and circle criterion for stability of nonlinear systems. The results clearly determine the extent of input~output stability, i.e. the set of input.[hnctions./br which stability is 9uaranteed.

F is the field IR of real numbers.

We will make the following assumptions regarding the space X :

(i) X is a binormed space, with primary and secondary norms I1"11.~, and II'll,~, respectively. (ii) X is closed under the family of truncations {(')r}. In other words, if x e X, then XT~f , VT~ ~. (iii) Ifx6f, and T~ ~, then [[XT[[U" <~ I[XI[:7", and [IXT[I,~ ~< [Ixll...

(iv) If x~Xe, then x~X if and only if limv~llxr[[e-< ~, and limr~l]xr[}, <00.