Computing the Domain of Attraction of Switching Systems Subject to Non-Convex Constraints

Nikolaos Athanasopoulos, Raphaël M. Jungers
2016 Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control - HSCC '16  
We characterize and compute the maximal admissible positively invariant set for asymptotically stable constrained switching linear systems. Motivated by practical problems found, e.g., in obstacle avoidance, power electronics and nonlinear switching systems, in our setting the constraint set is formed by a finite number of polynomial inequalities. First, we observe that the so-called Veronese lifting allows to represent the constraint set as a polyhedral set. Next, by exploiting the fact that
more » ... e lifted system dynamics remains linear, we establish a method based on reachability computations to characterize and compute the maximal admissible invariant set, which coincides with the domain of attraction when the system is asymptotically stable. After developing the necessary theoretical background, we propose algorithmic procedures for its exact computation, based on linear or semidefinite programs. The approach is illustrated in several numerical examples. Keywords semi-algebraic constraints, switching linear systems, domain of attraction, maximal admissible invariant set, algorithms
doi:10.1145/2883817.2883823 dblp:conf/hybrid/AthanasopoulosJ16 fatcat:2vrv3ebhefcsdplzhxbgpq4bkm