A new approach to the stability of nonlinear systems with uncertain plant parameters

Tan N., Atherton D.

Annual American Control Conference (ACC 2003), Colorado, United States Of America, 04 June 2003 - 06 June 2006, pp.1843-1848 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume:
  • City: Colorado
  • Country: United States Of America
  • Page Numbers: pp.1843-1848
  • Inonu University Affiliated: Yes


The purpose of this paper is to study the problem of the stability of nonlinear systems with variable plant parameters. A new approach which enables one to predict the existence of limit cycles in a control system which simultaneously contains nonlinearities and parametric uncertainties is given. The proposed method makes use of the popular describing function technique and the Bode envelope of linear uncertain transfer functions. The narrowest possible Bode envelopes are obtained from new results obtained by the authors where the plant transfer function is taken in factored form. The technique can be used to cover the cases of linear elements, which have multilinear or nonlinear uncertainty structure, and a nonlinear element with or without memory. Examples are given to show how the proposed method can be used to assess the stability of nonlinear systems with uncertain plant parameters.