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

Verghese, George C.; Lévy, Bernard C.; Kailath, Thomas

IEEE Trans. Autom. Control 26, 811-831 (1981).

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

Keywords:

controllability; observability; equivalence