Pole Assignment Problem for Discrete-Time Descriptor Systems with Period 3 by Derivative and Proportional State Feedback

• Main Authors: Jr-Wei Yang, 楊志偉
• Other Authors: Wen-Wei Lin
• Format: Others
• Language: en_US
• Published: 2003
• Online Access: http://ndltd.ncl.edu.tw/handle/57534156790815869435

碩士 === 國立清華大學 === 數學系 === 91 === In this paper we investigate the pole assignment problem for discrete-time descriptor systems with period 3 by derivative and proportional state feedback. The results in this paper are quote from [3], [8] and [16], respectively. In section 1 we review the definitions and results of the descriptor system with period 1. In section 2 we introduce the definitions of the descriptor systems with period 3. In section 3 we introduce some notations and examine how the response of the periodic descriptor systems depend on the eigenstructure of the associated periodic matrix pairs {(E_j,A_j)}_{j=1}^{3}, that is (2.3). Definitions of complete and strong reachability are given and the significance of these conditions are discussed. In section 4 we present an algorithm to reduce the periodic matrix triples {E_j,A_j,B_j}_{j=1}^{3} into canonical forms by using orthogonal and elementary matrix transformations. In section 5 we shown that a periodic descriptor systems that is strongly reachable can be transformed into a regular systems and of index at most 1 by derivative and proportional state feedback. In section 6 applications to the pole assignment problem are discussed, this is our main result of this paper. The extend to which the poles can be assigned by derivative and proportional state feedback whilst retaining regularity is examined under the different reachability conditions.