A generalized state-space for singular systems.(English)Zbl 0541.34040

The paper deals with linear systems that can be described by means of the equations $$E\dot x(t)=Ax(t)+Bu(t),\quad y(t)=Cx(t), t>0$$, where the matrix E is singular. Several concepts known from the case when E is nonsingular are adequately extended to the singular case. For instance, the concepts of controllability and observability are discussed. Also, a concept of (strong) equivalence is proposed. It is then shown that two systems are strongly equivalent, if and only if they have the same transfer function. A rich bibliography is given, and connections with previous results are illustrated.
Reviewer: C.Corduneanu

MSC:

 34H05 Control problems involving ordinary differential equations 93B05 Controllability
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