A local theory of inputoutput stability of dynamical systems文档.pdf

A local theory of inputoutput stability of dynamical systems文档.pdf

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A local theory of inputoutput stability of dynamical systems文档

A Local TheoryofInput/Output Stability of Dynamical Systems by H O R A C I O MARQUEZ~ Department of Enyineering, Royal Roads Military College, F M O Victoria, British Columbia, VOS 1BO, Canada ABSTRACT: Thepurpose of this paper is topresent a local theory of input/output stability OJ dynamical systems. More precisely, the intention is to obtain local open loop conditionsfor local closed loop stability offeedback interconnections. It will be shown that, by setting the problem in the context of extended binormed spaces it ispossible to obtain local versions of the so-called small 9ain theorem and circle criterionfor 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. L Introduction In this paper we are concerned with stability of dynamical systems. Roughly speaking, there are two conceptually different approaches to stability theory: (i) Lyapunov theory, and (ii) the input/output approach. The former studies the stability of an equilibrium state of the autonomous, or unforced system, while the latter regards systems as mappinys between inputs and outputs. The Lyapunov theory was initiated by A. M. Lyapunov in the 1890s and it is summarized in several textbooks [see for example (1-3)], while the input/output theory was initiated in the 1960s by G. Zames (4, 5), and I. Sandberg (6, 7). See also references (8, 9) for thorough expositions of the input/output theory. Intrinsic in the philosophical differences between these two approaches is the fact that, while the Lyapunov theory is es

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