| Summary: | 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.
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