Decentralized stabilization for expanding construction of large-scale systems

A decentralized stabilization problem compatible with expanding the construction of large-scale systems is considered. It is assumed that a large-scale system is obtained by adding new subsystems one after another. When a new subsystem is connected to an already interconnected portion, a local controller is designed for the new subsystem so that both the subsystem and the resultant expanded system are stable. The proper-stable-factorization approach is used for calculating the local controllers. Sufficient conditions on subsystems for such stabilization are presented. They are expressed in terms of the solvability of linear matrix equations over the ring of stable rational matrices