Stabilization of Linear Systems with Structured Perturbations

Abstract

The problem of stabilization of linear systems with bounded structured uncertainties are considered in this paper. Two notions of stability, denoted quadratic stability (Q-stability) and stability, are considered, and corresponding notions of stabilizability and detectability are defined. In both cases, the output feedback stabilization problem is reduced via a separation argument to two simpler problems: full information (I) and full control (FC). The set of all stabilizing controllers can be parametrized as a linear fractional transformation (LFT) on a free stable parameter. For Q-stability, stabilizability and detectability can in turn be characterized by Linear Matrix Inequalities (LMIs), and the FI and FC Q-stabilization problems can be solved using the corresponding LMIs. In the standard one-dimensional case the results in this paper reduce to well-known results on controller parametrization using state-space methods, although the development here relies more heavily on elegant LFT machinery and avoids the need for coprime factorizations.

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Document Details

Document Type
Technical Report
Publication Date
Apr 11, 1993
Accession Number
ADA465127

Entities

People

  • John Doyle
  • Kemin Zhou
  • Wei-min Lu

Organizations

  • California Institute of Technology

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Abstracts
  • Closed Loop Systems
  • Construction
  • Control Systems
  • Engineering
  • Equations
  • Feedback
  • Frequency
  • Inequalities
  • Linear Systems
  • Materials
  • Notation
  • Perturbations
  • Standards
  • Structural Properties
  • Transfer Functions
  • Uncertainty

Fields of Study

  • Mathematics

Readers

  • Control Systems Engineering.
  • Mathematical Modeling and Probability Theory.
  • Operations Research

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