Stability analysis and state feedback stabilization of pendulum-like systems with multiple nonlinearities

Hua Ouyang, Ian R. Petersen, Valery Ugrinovskii

Research output: Contribution to journalArticle

2 Citations (Scopus)


This paper addresses the Lagrange stability analysis problem and the state feedback Lagrange stabilization problem for pendulum-like systems with multiple nonlinearities. An existing method for analysing the Lagrange stability of pendulum-like systems with a single nonlinearity is generalized to pendulum-like systems with multiple nonlinearities. Also, a non-degeneracy condition of the existing Lagrange stability criterion is removed and a strict frequency-domain inequality is used instead. To study the state feedback Lagrange stabilization problem, this paper develops an extended strict bounded real lemma for linear systems which are not stable but stabilizable. A sufficient condition for state feedback Lagrange stabilization is proposed in terms of an algebraic Riccati equation with a sign indefinite solution.

Original languageEnglish
Pages (from-to)2235-2243
Number of pages9
Issue number9
Publication statusPublished - Sep 1 2012



  • Extended strict bounded real lemma
  • Lagrange stability
  • Multiple equilibria
  • Multiple nonlinearities
  • Pendulum-like systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering

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