Guaranteed domains of attraction for multivariable luré systems via open Lyapunov surfaces

Wassim M. Haddad, Vikram Kapila, Vijaya Sekhar Chellaboina

Research output: Contribution to journalArticlepeer-review


In this paper we provide guaranteed stability regions for multivariable Luré-type systems. Specifically, using the Luré-Postnikov Lyapunov function a guaranteed subset of the domain of attraction for a feedback system whose forward path contains a dynamic linear time-invariant system and whose feedback path contains multiple sector-bounded time-invariant memoryless nonlinearities is constructed via open Lyapunov surfaces. It is shown that the use of open Lyapunov surfaces yields a considerable improvement over closed Lyapunov surfaces in estimating the domain of attraction of the zero solution of the nonlinear system. An immediate application of this result is the computation of transient stability regions for multimachine power systems and computation of stability regions of anti-windup controllers for systems subject to input saturation.

Original languageEnglish (US)
Pages (from-to)935-949
Number of pages15
JournalInternational Journal of Robust and Nonlinear Control
Issue number10
StatePublished - Oct 1997


  • Absolute stability
  • Domains of attraction
  • Lyapunov surfaces
  • Multivariable systems
  • Popov criterion
  • Stability regions

ASJC Scopus subject areas

  • Control and Systems Engineering
  • General Chemical Engineering
  • Biomedical Engineering
  • Aerospace Engineering
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering
  • Electrical and Electronic Engineering


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