Decentralized control of interconnected dynamical systems

In this paper we consider the decentralized stabilization problem for a class of large systems formed by the dynamic interconnection of several multivariable systems. For this structured class of systems, we establish the conditions under which the interconnected system is controllable and observable. We then simplify and interpret these conditions to obtain simple sufficient conditions that guarantee controllability and observability in terms of the subsystem and interconnection subsystem coefficient matrices. Also, the conditions under which stabilization using decentralized feedback is possible are explicitly stated. We then simplify these to obtain sufficient conditions at the subsystem level. These conditions imply that if the interaction subsystems are stable and, in addition, certain mild restrictions on the subsystems and the interconnections hold, then the large system is stabilizable with decentralized feedback. Finally, we state the sufficient conditions for stabilizing this class of systems via local state feedback.