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An improved algorithm for the computation of structural invariants of a system pencil and related geometric aspects

✍ Scribed by C. Oară; P. Van Dooren

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
696 KB
Volume
30
Category
Article
ISSN
0167-6911

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✦ Synopsis

In this paper we propose a new recursive algorithm for computing the staircase form of a matrix pencil, and implicitly its Kronecker structure. The algorithm compares favorably to existing ones in terms of elegance, versatility, and complexity. In particular, the algorittun without any modification yields the structural invariants associated with a generalized state-space system and its system pencil. Two related geometric aspects are also discussed: we show that an appropriate choice of a set of nested spaces related to the pencil leads directly to the staircase form; we extend the notion of deflating subspace to the singular pencil case.

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