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External Stabilizability of Nonlinear Systems with Some Applications

By Andrea Bacciotti

Abstract

: The aim of this paper is to discuss the existence of suitable feedback laws which provide stability (in a technical sense to be specified) with respect to inputs and initial conditions of the state response of a nonlinear system. 1. Introduction Roughly speaking, a forced system is said to be externally stable if the future state evolution is bounded whenever the input is bounded. Moreover, the system is said to be externally stabilizable if the external stability property can be achieved by means of some state static feedback connection. As the classical theory of linear systems shows, external stability and stabilizability are related to the so-called internal stability properties, that is stability properties of the associated unforced system. In this work we consider nonlinear systems of the form (1) x = f(x; u) where x 2 R n , u 2 R m and f 2 C 1 (R n \Theta R m ; R n ). Admissible inputs are piecewise continuous, bounded functions u : [0; +1) ! R m . The associ..

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