Accession Number:

AD0759271

Title:

Controllability and Observability in Banach Space with Bounded Operators,

Descriptive Note:

Corporate Author:

MINNESOTA UNIV MINNEAPOLIS DEPT OF ELECTRICAL ENGINEERING

Personal Author(s):

• Triggiani,Roberto

Report Date:

1973-02-01

Pagination or Media Count:

53.0

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 Hahn-Banach 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 integro-differential equations of Volterra type, the present theory leads in turn to explicit, easy-to-check 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