On U(�)-invariance for finite and infinite dimensional control systems

Abstract

The purpose of this paper is to study the property of set invariance in connection with finite and infinite dimensional, nonlinear control systems. Our work was motivated by the papers of Feuer-Heymann [5], [6], who investigated this problem in the context of nonlinear, finite dimensional control systems. Using some recent results and techniques from the theory of multifunctions and the theory of differential inclusions, we are able to relax some of the restrictive hypotheses that Feuer-Heymann [5], [6] have and also consider infinite dimensional control systems (distributed parameter systems). In the next section, we establish our notation and recall some basic definitions and facts from nonsmooth analysis and the theory of multifunctions. In Section 3 we study the problem of U(.)-invariance for nonlinear, finite dimensional control systems, extending the works of Feuer-Heymann [5], [6]. Finally, in Section 4 we address similar questions in the context of infinite dimensional, generally nonlinear, control systems.