A new decentralized stabilization design for large-scale systems

A decentralized stabilization problem for a large-scale system composed of a number of subsystems is investigated. Using Lyapunov stability and the bounds of the solution of the Lyapunov equation, we derive two main results. The first result (Theorem 1) requires checking the negativity of a matrix containing two free parameters to test the decentralized stabilizability of the whole system. The second result (Theorem 2) determines the ranges of two free parameters to satisfy Theorem 1 such that the decentralized local state feedbacks guarantee the whole large-scale system is stabilized. The matching condition for each subsystem is not necessary in this paper. The results are also summarized using a flow chart which represents the algorithm for decentralized stabilization.