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

Wassim M. Haddad, Vikram Kapila, Vijaya Sekhar Chellaboina

Research output: Contribution to journalArticle

Abstract

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
Volume7
Issue number10
StatePublished - Oct 1997

Fingerprint

Multivariable systems
Stability Region
Domain of Attraction
Open Systems
Lyapunov
Input Saturation
Feedback
Path
Invariant
Feedback Systems
Lyapunov functions
Set theory
Type Systems
Power System
Lyapunov Function
Linear Time
Nonlinear systems
Sector
Nonlinear Systems
Nonlinearity

Keywords

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

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering
  • Applied Mathematics

Cite this

Guaranteed domains of attraction for multivariable luré systems via open Lyapunov surfaces. / Haddad, Wassim M.; Kapila, Vikram; Chellaboina, Vijaya Sekhar.

In: International Journal of Robust and Nonlinear Control, Vol. 7, No. 10, 10.1997, p. 935-949.

Research output: Contribution to journalArticle

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