Polynomial systems and Kronecker invariants. (English) Zbl 0617.93005
The Kronecker canonical form is generalized from the set of matrix pencils to the set of all the rational matrix functions \(W(\lambda)=\sum^{\ell}_{i=-\infty}W_ i\lambda^ i\), in a way which depends on the choice of \(\ell \in {\mathbb{N}}\). If a polynomial system \(W(\lambda)=C(\lambda I-A)^{-1}B+\sum^{\ell}_{i=0}W_ i\lambda^ i\) is given as a partial realization for W, the \(\ell\)-Kronecker form of W is shown to be equal to the classical Kronecker form of the companion pencil. This invariance property fails if we replace the Kronecker form by the McMillan canonical form.
MSC:
93B10 | Canonical structure |
15A21 | Canonical forms, reductions, classification |
93C05 | Linear systems in control theory |
93B15 | Realizations from input-output data |
Keywords:
Kronecker canonical form; matrix pencils; rational matrix functions; polynomial system; McMillan canonical formReferences:
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