Computation of limit cycles for uncertain nonlinear fractional-order systems

The present paper proposes an algorithm to compute limit cycle points for an uncertain nonlinear fractional-order system with separable nonlinearities using interval constraint propagation. It is first shown that the problem of finding limit cycle points can be formulated as an interval constraint satisfaction problem and then solved using the branch and prune algorithm. The algorithm guarantees that all the points on the limit cycle locus are computed to the prescribed accuracy. The proposed algorithm is demonstrated with a fractional commensurate order system with uncertain coefficients and also with a practical application of a gas turbine plant.