An Algebraic Approach to Time Scale Analysis and Control.

Abstract

An algebraic approach is developed for multiple time scale decomposition of a linear system using the Smith structure of the system matrix viewed as the matrix of functions of a small parameter c. This derivation makes clear that both the necessary and sufficient multiple semi-stability (MSST) condition, which ensures well-defined multiple time scale behavior and the time-scale-decomposed system structure which approximates the original system are closely related to the so-called Schur complements of a certain matrix. Furthermore, this decomposition has been extended to a larger class of systems, satisfying the so-called multiple semi-simple nullstructure (MSSNS) condition. The algebraic approach is also applied to examine the questions of the feedback control of the linear systems. Specifically this document presents results on time scale modifications by state feedback. Keywords: Theses eigenvalues; perturbations.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1985
Accession Number
ADA162806

Entities

People

  • Xi-cheng Lou

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Air Platforms
  • C4I
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Boundary Layer
  • Classification
  • Closed Loop Systems
  • Computations
  • Decomposition
  • Differential Equations
  • Eigenvalues
  • Electrical Engineering
  • Engineering
  • Equations
  • Feedback
  • High Gain
  • Linear Differential Equations
  • Linear Systems
  • Real Variables
  • Stability Conditions

Fields of Study

  • Mathematics

Readers

  • Control Systems Engineering.
  • Linear Algebra
  • Theoretical Analysis.