# Accession Number:

## AD0738097

# Title:

## The Linear Stabilization Problem in Hilbert Space,

# Descriptive Note:

# Corporate Author:

## BROWN UNIV PROVIDENCE R I DIV OF APPLIED MATHEMATICS

# Personal Author(s):

# Report Date:

## 1971-01-01

# Pagination or Media Count:

## 21.0

# Abstract:

The paper considers the linear control system dxdt Ax Bu. Here A is infinitesimal generator of a strongly continuous group of bounded linear operators Tt 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 ut Kxt 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:

# Subject Categories:

- Theoretical Mathematics