An Interval Approach to Compute Invariant Sets

This paper proposes an original interval-based method to compute an outer approximation of all invariant sets (such as limit cycles) of a continuous-time nonlinear dynamic system, which are included inside a prior set of the state space. Contrary to all other existing approaches, our method has the following properties: first, it is guaranteed (a solution cannot be lost); second, it is applicable to a large class of systems without any specific assumption such as the knowledge of a Lyapunov function or any partial linearity; and third, there is no need to integrate the system.