Stability of Large Scale Systems Under Decentralized Control

Abstract

The problem dealt with in this paper is the decentralized stabilization of linear continuous-time large scale systems (LSS) by static state feedbacks. The suggested approach consists in an additional decomposition of the local subsystems, usage of bounds on the solution of Lyapunov matrix equation, vector Lyapunov function and the comparison principle. Our main purpose is to overcome two important shortcomings of the existing approaches: the requirement for solution of Riccati (Lyapunov) matrix equations at each iteration, which may be time consuming and the a priori unawareness of this solution, involved in the stability condition. The main result is a sufficient stability condition, whose outstanding feature is flexibility. The validity of the approach and its capabilities are illustrated on the error regulation problem of a string of moving vehicles.