Analysis and Design of Controllers for Robust Stability of Interconnected Discrete Systems

This paper presents sufficient conditions for the stability of interconnected discrete systems and interconnected uncertain discrete systems. These results use a recently developed bound on elemental (structured) time-varying perturbations of an asymptotically stable linear time-invariant discrete system, based on Lyapunov theory and singular value decomposition techniques. These stability bounds are then used in the design of controllers for interconnected uncertain discrete systems. Two types of controller designs are considered. The first is a local-controller (sub-system level) based on linear regulator theory. The second is a two-level controller (local and global). These new results are also illustrated with simple examples.