Decentralized stabilization of large-scale linear parameter varying systems

Abstract

In stabilization of a Large-Scale System (LSS), the decentralized nature of the controller is a significant issue, because centralized controllers are difficult and impractical for real-time implementation. The designing procedure for decentralized controllers should guarantee the stability of the overall LSS and at the same time, allow limited information exchange in the LSS. In this paper, a decentralized controller for a nonlinear LSS modeled by a Linear Parameter Varying (LPV) model is designed. The controller design procedure is formulated as a convex feasibility problem which can be solved by finding a feasible answer to some Linear Matrix Inequalities (LMIs). The solution to this feasibility problem assures a fully decentralized controller where information exchange among local controllers is forbidden and, only data transfer among each controller and its corresponding subsystem is allowed. In the proposed approach, the Lyapunov function of the LSS equipped with local controllers is considered as the sum of the Lyapunov functions of all subsystems. Then, the stability conditions are derived to assure the stability of the LSS. After designing a decentralized controller to ensure LSS stability, the same approach is exploited for H∞ and H2 performance improvement of the LSS in the presence of disturbances. To verify the efficacy of the designed controller, a large-scale power system which is a practical example is considered, and the proposed approach is applied on it. The simulation results prove the appropriateness of the designed local controllers.