Control Synthesis for the Large-Scale System Based on a Linear Decomposition of Nonlinear Interconnections

This paper studies the H control problem for a nonlinear large-scale system with unknown disturbance. In the large-scale system, each subsystem “without” nonlinear interconnections and disturbance is transformed into a T-S fuzzy system. Moreover, based on a linear decomposition, the nonlinear interconnection corresponding to each subsystem is decomposed to a linear weighting interconnection which contains a fixed linear term and an uncertain linear term. Based on the above transformation, the total fuzzy rules’ number of the transformed large-scale system is reduced evidently so that the rule explosion problem will be avoided. In this study, some conditions are proposed to guarantee the existence of Parallel Distributed Compensation (PDC) fuzzy controllers and then the controllers using Linear Matrix Inequality (LMI) tool are synthesized such that the H control performance of the nonlinear large-scale system is achieved. Finally, a numerical example and a balancing double-inverted pendulums example are given to demonstrate the effectiveness of the controller.