Accession Number:

ADA459985

Title:

Conditions for Scale-Based Decompositions in Singularly Perturbed Systems

Descriptive Note:

Corporate Author:

MASSACHUSETTS INST OF TECH CAMBRIDGE DEPT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE

Report Date:

1987-02-01

Pagination or Media Count:

26.0

Abstract:

Singularly perturbed models of the form xt Aepsilonxt, with Aepsilon analytic at 0, nonsingular for epsilon Epsilon 0, epsilon 0 and singular at epsilon 0, arise naturally in various problems of systems and control theory. Under a so-called multiple semi-simple null structure or MSSNS condition on Aepsilon, the eigenstructure of this matrix has a multiple scale property that allows the asymptotic eigenstructure of the matrix to be studied via reduced-order matrices associated with the separate scales. Under a stronger multiple semi-stability or MSST condition, this eigenstructure decomposition translates into a time-scale decomposition of the solution xt of the system. This paper is aimed at illuminating the MSSNS and MSST conditions.

Subject Categories:

  • Numerical Mathematics
  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE