A behavioral approach to singular systems (Q1281456)

The behavioral approach to linear systems has received a great deal of attention since it was first introduced by \textit{J. C. Willems} [Automatica 22, 561-580 (1986; Zbl 0604.62090)]. In the present paper, abstract linear behaviors are defined as generalization of Willems' behaviors. This new notion allows a description of singular systems in a very natural way. It is shown that there is a one-to-one correspondence between the class of abstract linear behaviors and coherent sheaves on the projective line. Realization theory is studied in this setting and the paper ends with definitions of controllability and observability based on abstract linear behaviors.