A computational approach for estimating stability regions

In this paper, we propose a computational approach for estimating the stability region of an asymptotically stable equilibrium point. The stability region is estimated through an iterative process specified as an algorithm. Reachable sets are used in the estimation algorithm for checking the invariant property of the initial estimate of a stability region and for representing the enlarged stability regions. The convergence of the estimation algorithm can be shown by considering the sequence properties of the reachable sets. Level set methods are used for representing reachable sets and tracking the evolution of the boundary of a reachable set since they can be used to effectively represent complex continuous sets and, furthermore, there exist efficient computation methods for computing the evolution of reachable sets for nonlinear systems. The proposed approach allows natural extension to higher dimensional systems and enables the computation to be carried out in a parallel manner. ReachLab, a model-based tool, is developed to enable rapid prototyping of the algorithm, and to allow the use of various computation methods for implementing the algorithm on a cluster of parallel computing machines. The accuracy of the proposed approach is compared with another accurate approach. The computation results for three nonlinear systems are presented.