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
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