An algorithm for computing the staircase form of a system pencil and related geometric aspects

Oara, Cristian;Van Dooren, Paul
(1996) Proceedings IEEE CDC 96 — Location: Kobe - Japan

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  • Oara, CristianUCLouvain
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  • Van Dooren, PaulUCLouvain
    Author
Abstract
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 algorithm 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; and we extend the notion of deflating subspace to the singular pencil case
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Oara, C., & Van Dooren, P. (1996). An algorithm for computing the staircase form of a system pencil and related geometric aspects. Proceedings IEEE CDC 96, Kobe - Japan. https://hdl.handle.net/2078.5/222804