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Minimal representations of implicit linear systems. (English) Zbl 0565.93012
The paper investigates a generalized linear system description with the purpose i) to establish a set of simple conditions necessary and sufficient for the linear system model to be minimal in a certain well- defined sense, and ii) to set up a stable algorithm for deriving a minimal representation from a non-minimal one.
The conditions for minimality are formulated in four properties concerning row- as well as column regularities of matrices which form the partitioned coefficient matrix of the associated homogeneous linear system. So, four rank tests are needed to check minimality. Two of them correspond to generalizations of controllability and observability criteria, the third one corresponds to removal of system poles at infinity, and the last one takes into account the set of algebraically dependent variables. For linear state-space models two of the four criteria are always valid. The four steps in the minimization algorithm correspond to the four properties necessary for minimality. A pseudo- algorithmic language is used for description of the procedures. They are tested in an illustrative numerical example.
Reviewer: H.D.Fischer

93B20 Minimal systems representations
93B40 Computational methods in systems theory (MSC2010)
93C05 Linear systems in control theory
15A03 Vector spaces, linear dependence, rank, lineability
34A99 General theory for ordinary differential equations
65J10 Numerical solutions to equations with linear operators
Full Text: DOI
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