
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 wellknown 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