Construction of a Contraction Metric for Time-Periodic Systems Using Meshless Collocation

The existence and stability of a periodic orbit for time-periodic systems as well as its basin of attraction can be determined using a contraction metric. In this letter, we will present a numerical construction method based on meshless collocation with radial basis functions. We will first show the existence of a contraction metric satisfying a partial differential equation and then use meshless collocation to approximately solve it, which results in a contraction metric, if the fill distance is sufficiently small.