
Accession Number : AD0759271
Title : Controllability and Observability in Banach Space with Bounded Operators,
Corporate Author : MINNESOTA UNIV MINNEAPOLIS DEPT OF ELECTRICAL ENGINEERING
Personal Author(s) : Triggiani,Roberto
Report Date : FEB 1973
Pagination or Media Count : 53
Abstract : The classical theory of (state and output) controllability and observability in finite dimensional spaces is extended to linear abstract systems defined on infinite dimensional Banach spaces, under the basic assumption that the operator acting on the state be bounded. Tests for approximate controllability as well as observability, expressed only in terms of the coefficients of the system, are proved via a consequence of the HahnBanach theorem, and new phenomena arising in infinite dimensions are studied: for instance, by using Baire category arguments, it is shown that state exact controllability, under large conditions met in cases of physical interest, never arises in infinite dimensional Banach spaces, even with free final instant. Several examples are presented throughout; in particular, for dynamical systems modeled by integrodifferential equations of Volterra type, the present theory leads in turn to explicit, easytocheck criteria for approximate controllability and observability. (Author)
Descriptors : (*ADAPTIVE CONTROL SYSTEMS, MATHEMATICAL MODELS), LINEAR SYSTEMS, BANACH SPACE, DIFFERENTIAL EQUATIONS, INTEGRAL EQUATIONS, THEOREMS, THESES
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE