Abstract
In this paper we investigate the pole assignment problem fordiscrete-time descriptor systems with period 3 by derivative andproportional state feedback. The results in this paper are quotefrom [3], [8] and [16], respectively.In section 1 we review the definitions and results of thedescriptor system with period 1. In section 2 we introduce thedefinitions of the descriptor systems with period 3. In section 3we introduce some notations and examine how the response of theperiodic descriptor systems depend on the eigenstructure of theassociated periodic matrix pairs {(E_j,A_j)}_{j=1}^{3}, thatis (2.3). Definitions of complete and strong reachability aregiven and the significance of these conditions are discussed. Insection 4 we present an algorithm to reduce the periodic matrixtriples {E_j,A_j,B_j}_{j=1}^{3} into canonical forms by usingorthogonal and elementary matrix transformations. In section 5 weshown that a periodic descriptor systems that is stronglyreachable can be transformed into a regular systems and of indexat most 1 by derivative and proportional state feedback. Insection 6 applications to the pole assignment problem arediscussed, this is our main result of this paper. The extend towhich the poles can be assigned by derivative and proportionalstate feedback whilst retaining regularity is examined under thedifferent reachability conditions.