Descriptor Variable and Generalized Singularly Perturbed Systems: A Geometric Approach.

Abstract

Existing results in descriptor variable theory are interpreted geometrically. New results are obtained concerning linear feedback and pole placement in such systems. Descriptor variable systems are viewed as limits of singularly perturbed systems. It is shown that some important singularly perturbed systems cannot be treated effectively with standard techniques. Hence, a generalized class of singularly perturbed systems is considered. A geometric decomposition that preserves continuity about the singular point is derived. Conditions are presented under which the solution of a singularly perturbed system converges with the parameter. Miscellaneous structural properties are established with applications to the quadratic regulator problem. (Author)

Open PDF

Document Details

Document Type
Technical Report
Publication Date
May 01, 1980
Accession Number
ADA123970

Entities

People

  • J. Daniel Cobb

Organizations

  • University of Illinois Urbana–Champaign

Tags

Communities of Interest

  • Advanced Electronics
  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Closed Loop Systems
  • Differential Equations
  • Electrical Engineering
  • Engineering
  • Equations
  • Feedback
  • Geometry
  • Hilbert Space
  • Perturbation Theory
  • Standards
  • Structural Properties
  • Theorems
  • Topology
  • United States
  • Universities
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Calculus or Mathematical Analysis