A Polynomial-time Algorithm for Determining Quadratic Lyapunov Functions for Nonlinear Systems

Abstract

We consider nonlinear systems dx=dt = f(x(t)) where Df(x(t)) is known to lie in the convex hull of L matrices A(sub 1),..., A(sub L) Epsilon R(expn nxn). For such systems, quadratic Lyapunov functions can be determined using convex programming techniques. This paper describes an algorithm that either finds a quadratic Lyapunov function or terminates with a proof that no quadratic Lyapunov function exists. The algorithm is an interior-point method based on the theory developed by Nesterov and Nemirovsky.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1993
Accession Number
ADA640063

Entities

People

  • L. Vandenberghe
  • S. Boyd

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Computer Programming
  • Convex Programming
  • Electrical Engineering
  • Engineering
  • Information Operations
  • Iterations
  • Linear Programming
  • Lyapunov Functions
  • Mathematics
  • Nonlinear Systems
  • Optimization
  • Polynomials

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Operations Research