A local theory of input/output stability of dynamical systems

The purpose of this paper is to present a local theory of input/output stability of 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 gain 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 functions for which stability is guaranteed.