Reachability, Observability and Minimality for Shift-Invariant Two-Point Boundary-Value Descriptor Systems.

摘要

In this reprint we study the system-theoretic properties of two related classes of shift-invariant two-point boundary-value descriptor systems (TPBVDSs), namely displacement systems for which Green's function is shift-invariant, and stationary systems for which the input-output map is stationary. For such systems it is possible to obtain detailed characterizations of the properties of weak reachability and observability and of minimality as well. An important difference, that has also been noted before in a different context, is that there is a certain level of nonuniqueness in minimal realizations. Another property that is studied in this paper is that of extendibility, i.e., the concept of considering a TPBVDS as being defined on a sequence of intervals of increasing length. Necessary and sufficient conditions for extendibility are given. (kr)