Accession Number : AD0738097

Title :   The Linear Stabilization Problem in Hilbert Space,

Corporate Author : BROWN UNIV PROVIDENCE R I DIV OF APPLIED MATHEMATICS

Personal Author(s) : Slemrod,Marshall

Report Date : 1971

Pagination or Media Count : 21

Abstract : The paper considers the linear control system dx/dt = Ax + Bu. Here A is infinitesimal generator of a strongly continuous group of bounded linear operators T(t) on a Hilbert space E, B is a bounded linear operator from a Hilbert space H to E. The author gives sufficient conditions for the existence of a bounded linear operator K from E to H so that the control system with feedback control law u(t) = Kx(t) has the zero solution asymptotically stable. The results reduce to a well-known theorem of Kalman in the case E,H are finite dimensional. (Author)

Descriptors :   (*ADAPTIVE CONTROL SYSTEMS, MATHEMATICAL MODELS), HILBERT SPACE, LINEAR SYSTEMS, STABILITY, FEEDBACK, OPERATORS(MATHEMATICS)

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE