On the stability and control of discrete linear systems with clock synchronization errors

摘要

This paper considers discrete linear time-invariant systems that can be decomposed into subsystems whose states are synchronized by a common clock whose signal reaches them with delays. In particular, stability for the case where all subsystems have the same sampling frequency, but different switching times, is investigated. In contrast to previous work, the approach taken here models the set of system matrices that arise using a polytopic uncertainty approach, which has seen extensive application in robust control theory for linear systems. Stabilization is then achieved by state feedback and a method to handle the combinatorial explosion of the number of polytope vertices is developed and illustrated using an example from swarm system navigation.