Stability and robustness of systems with synchronization errors

This paper addresses the problem of synchronization errors in distributed dynamical systems. In particular, it focuses on the question of stability for the case where all subsystems have the same sampling frequency, but different switching times. In contrast to previous work, the approach taken here models the set of system matrices that arise using a polytopic uncertainty approach, where a polytope vertex corresponds to a possible state matrix of the overall system. System stabilization is then approached through state feedback and LMI techniques are used to generate the control law matrices. A method to handle the combinatorial explosion of the number of polytope vertices is developed and illustrated using an example from swarm system navigation.