A TOEPLITZ CHARACTERIZATION OF THE STA TICOUTPUT FEEDBACK STABILIZATION SYSTEMS PROBLEM FOR LINEAR DISCRETE-TIME A. Astolfi*o, P . Colanerf * Politecnico di Milano Dipartimento di Elettronic a e Informazione colaneri@elet.polimi. it ODept. of Electrical and Electronic Eng. - Imperial College Exhibition Road, London SW7 2BT, England (UK) a. astolfi@ic.uc.uk Piazza Leonar do da Vinci 32, 2Md8no (Italy) Abstract: The static output feedback (SOF) stabilization problem for linear SIMO or MISO discrete-time systems is presented and characterized in terms of the properties of positiv edefinite T oeplitzmatrices. A global minimization problem in a compact sets is introduced whose solution, if any, guarantees closed-loop stabilit y and the fulfillment of an upper bound to a suitable closed loop performance. 1. INTRODUCTION The static output feedback stabilization problem is one of the most known and still open issues in systems and control, see [I] for a recen tsurvey. Here we deal with a discrete-time linear system where x E lRn, u E lRm, y E lRP are the state, input and output vectors, respectively, and A, B, C are matrices with constant real coefficients and appropriate dimensions. The static output feedback stabilization problem for systen(1)-(2) consists in finding, if possible, a static control law described ly equations of the form such that the closed-loop system is asymptoti- cally stable, i.e. the matrix A + BFC has all its eigen dues with modulus less than one. If suc h an output feedback does exist, w esay that the system (1)-(2) is output stabilizable and that F is a solution of the problem. We make the assumptions that the system is observable and that C has full row rank. In particular, it is possible to define the projection matrix v = I - c’(cc’)-lc, whose role will be clear in the sequel. In this paper w eaim at characterizing the SOF problem as a constrained LMI problem and, at the same time, we propose an algorithm for MISO sys- tems based on the properties of positive Toeplitz matrices. The paper is organized as follows. In Section 2 w e give some preliminary results, namely tw o necessary and sufficient conditions for the solv- abilit yof the SOF stabilization problem for sys- Copyright © 2002 IFAC 195 www.elsevier.com/locate/ifac Copyright © 2002 IFAC 15th Triennial World Congress, Barcelona, Spain