April 24, 2006
Paul Fuhrmann
Title: On the state of behaviors
The theme of the talk is the study of the concept of state and the corresponding state maps in the context of Willems' behavioral theory. We concentrate on Markovian system and their representation in terms of first order difference or differential systems. We follow by a full analysis of the special case of state systems, the embedding of a linear system in a state system via the use of state maps arriving at state representations or, equivalently, to a realization theory for behaviors. Minimality is defined and characterized and a state space isomorphism theorem is established. Realization procedures based on the shift realization are developed as well as a rigorous analysis of the construction of state maps. The results presented are joint work with Y. Yamamoto and P. Rapisarda and owe much to Rapisarda and Willems [1997].