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Preprint 21-2006

Algebraic characterization of controllability and observability for second order descriptor systems

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

Author(s) : Philip Losse , Volker Mehrmann

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 21-2006

MSC 2000

93B05 Controllability
93B07 Observability

Abstract :
We analyze controllability and observability conditions for second order descriptor systems and show how the classical conditions for first order systems can be generalized to this case. We show that performing a classical transformation to first order form may destroy some controllability and observability properties. To avoid this, we will derive a canonical form and new first order formulations that do not destroy the controllability and observability properties. As an example, we demonstrate that the loss of impulse controllability in constrained multi-body systems is due to the representation as first order system.

Keywords : descriptor system, impulse controllability, impulse observability, second order system, order reduction, index reduction

Notes :
This is a corrected version of the preprint 21-2006 of October 2006

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