Robust distributed control of decomposable systems with switching network topology

In this paper, we consider the problem of designing distributed controller for networks of dynamic systems called decomposable systems with switching network topologies. Exploiting certain structural property associated with state space matrices of these systems, a modal decomposition approach is used to design a distributed controller that has the same interconnection structure as the networks in each instance; i.e. controller structure changes according to network topologies without any delay. An explicit expression for computing the controller parameters is derived using LMI approach under H₂ or H_∞ criteria with D-stability property. Moreover, a simple sufficient condition for the existence of such a controller is provided that ensures the stability of the network with any arbitrary switching provided that the networks switch among a finite set of admissible topologies. The simulations results are provided to support the theoretical development.