Tan N.Atherton D.P.2024-08-042024-08-04200297839026617461474-6670https://doi.org/10.3182/20020721-6-es-1901.00259https://hdl.handle.net/11616/9167615th World Congress of the International Federation of Automatic Control, 2002 -- 21 July 2002 through 26 July 2002 -- 153189This paper studies the existence of limit cycles in a control system which contains nonlinearities and parametric uncertainties. The existence of limit cycles in a control system with a separable nonlinearity can be predicted using the describing function. In this paper, some of the well-known results developed in the area of parametric robust control are used together with the describing function method to analyze the stability problem of uncertain nonlinear systems. Based on the segment lemma, a stability result for a control system with an uncertain nonlinear element and a fixed linear element is first derived. Then, a polynomial method and a graphical method are proposed to determine how much one can perturb the coefficients of the linear element without causing the nonlinear system to have a limit cycle. Examples are given to illustrate the method presented. Copyright © 2002 IFAC.eninfo:eu-repo/semantics/openAccessDescribing functionsLimit cyclesNonlinear control systemsParametric variationRobust stabilityUncertain dynamic systemsConference Object151556010.3182/20020721-6-es-1901.002592-s2.0-84945577878N/A