Reliable and accurate algorithm to compute the limit cycle locus for uncertain nonlinear systems

A reliable and accurate algorithm is proposed to compute the so-called limit cycle locus for separable nonlinear systems with nonlinear parametric uncertainty. The limit cycle locus for a given uncertain parameter is the locus of the limit cycle points as the parameter varies over its range. The uncertain parameter may be associated with either the linear or nonlinear element in the system. The proposed algorithm makes use of the describing function analysis technique and tools of interval analysis for predicting the limit cycle behaviour. The capability of the proposed algorithm is demonstrated on an example that can not be readily solved using existing methods. An additional example shows how the proposed algorithm can also be applied to tune a controller to achieve a prescribed limit cycle behaviour