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Descriptor systems: Decomposition into forward and backward subsystems. (English) Zbl 0534.93013
This paper discusses the geometric structure of the linear discrete-time invariant dynamical system \(Ex_{k+1}=Ax_ k+Bu_ k\) where E, A are \(n\times n\) matrices and B is \(n\times n\). The pencil (E,A) is assumed regular. The key concept is a deflating subspace S. A deflating subspace S is one so that \(\dim \quad(ES+AS)=\dim \quad S\). Let \(\hat E=(\lambda E+A)^{-1}A\) where \(\lambda\) is chosen so that \(\lambda E+A\) is nonsingular. Note that the deflating subspaces of (E,A) are precisely the invariant subspaces of \(\hat E\) (this is implicit but not explicit in the paper). The paper presents a unifying geometric framework for known facts about descriptor systems.
Reviewer: S.L.Campbell

MSC:
93B25 Algebraic methods
15A21 Canonical forms, reductions, classification
34A99 General theory for ordinary differential equations
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
93C05 Linear systems in control theory
93C99 Model systems in control theory
93C55 Discrete-time control/observation systems
47A15 Invariant subspaces of linear operators
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