language: en

Global Stabilization of Linear Discrete-Time Systems with Bounded Feedback

Yudi Yang
IBM,
MD340 1311 Mamaroneck Ave White Plains, NY 10605
yudiy@vnet.ibm.com
Eduardo D. Sontag
Department of Mathematics Rutgers University
New Brunswick, NJ 08903
sontag@hilbert.rutgers.edu
Hector J. Sussmann
Department of Mathematics Rutgers University
New Brunswick, NJ 08903
sussmann@hilbert.rutgers.edu

Abstract This paper deals with the problem of global stabilization of linear discrete time systems by means of bounded feedback laws. The main result proved is an analog of one proved for the continuous time case by the authors, and shows that such stabilization is possible if and only if the system is stabilizable with arbitrary controls and the transition matrix has spectral radius less or equal to one. The proof provides in principle an algorithm for the construction of such feedback laws, which can be implemented either as cascades or as parallel connections ("single hidden layer neural networks") of simple saturation functions.

1 Introduction