Boundary-Value Descriptor Systems: Well-Posedness. Reachability, and Observability,
Abstract
This paper introduces the class of two-point boundary-value descriptor systems (TPBVDS), discrete-time systems described by possibly linear dynamics and a set of boundary conditions constraining the values of the system state at the two endpoints of the system's interval of definition. By introducing a standard form for regular pencils we obtain a new and simple generalized Cayley-Hamilton theorem that simplifies our investigation of well-posedness, Green's function solution, and reachability and observability that one can define for TPBVDS, associated with processes that propagate inward from and outward toward the boundaries. We investigate each of these in detail, obtaining, among other things, far simpler forms for the reachability and observability results found previously in literature. In addition we describe several methods for the efficient solution of TPBVDS, one involving recursions from each end of the interval toward the other and two others involving recursions that proceed outward toward and inward from the boundaries.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1986
- Accession Number
- ADA187473
Entities
People
- Alan S. Willsky
- Bernard C. Lévy
- Ramine Nikoukhah
Organizations
- Massachusetts Institute of Technology