An Algebraic Approach to Time Scale Analysis of Singularly Perturbed Linear Systems,
Abstract
This paper develops an algebraic approach to the multiple time scale analysis of perturbed linear systems based on the examination of the Smith form of the system matrix viewed as a matrix over a ring of functions in the perturbation parameter. This perspective allows us to obtain a strengthened version of the results of an earlier work and to provide a bridge between these complex but general results and previous explicit, conceptually simple, but somewhat restrictive results. In addition, the authors' algebraic framework allows them to investigate a variety of other problems. In this paper they study the problem of developing valid time scale decompositions in cases in which weak damping terms discarded in the approaches in earlier works must be retained. Also, this approach exposes the role of the invariant factors of the system matrix in determining its time scales. This leads naturally to the problem of time scale modification, i.e., invariant factor placement, via state feedback. A result along these lines is presented.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1986
- Accession Number
- ADA186040
Entities
People
- Alan S. Willsky
- George C. Verghese
- Xi-cheng Lou
Organizations
- Massachusetts Institute of Technology