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Preprint 02-2014

Computation of State Reachable Points of Descriptor Systems

Source file is available as :   Portable Document Format (PDF)

Author(s) : Subashish Datta , Volker Mehrmann

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 02-2014

MSC 2000

93A10 General systems
15A21 Canonical forms, reductions, classification

Abstract :
This paper considers the problem of computing the state reachable points, from the origin, of a linear constant coefficient descriptor system. A numerical algorithm is proposed that can be implemented to characterize the reachable set in a numerically stable way. The original descriptor system is transformed into strangeness-free system within the behavioral framework followed by a projection that separates the system into its differential and algebraic parts. It is shown that the computation of the image space of two matrices, associated with the projected system, is enough to compute the reachable set (from the origin). Moreover, a characterization is presented of all the inputs by which one can reach to any arbitrary points in the reachable set. The effectiveness of the proposed approach is demonstrated through numerical examples.

Keywords : Linear descriptor system, behavior formulation, strangeness-free formulation, reachability

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