Synchronization of coupled dynamic systems using fuzzy design approach

This paper proposes a brand new T-S fuzzy model-based approach to achieve synchronization of coupled dynamical systems. The T-S fuzzy models are given to exactly represent the coupled dynamical systems. Then the model-based fuzzy synchronization design is carried out for each subsystem utilizing the concept of parallel distributed compensation(PDC). We analyze the stability of the overall fuzzy synchronization system by applying Lyapunov stability theory and derive stability conditions by solving linear matrix inequalities (LMI) problem. The methodology proposed here can be applied to continuous-time and discrete-time dynamic systems. A well known example, the driven pendulum model is used for the demonstration. It is noted that the coupled pendulum system can be regarded as an important engineering application. Indeed it can simply represent a model of a robot arm or a robot foot. Several numerical simulations for the synchronization of coupled dynamical system illustrate the effectiveness of the proposed scheme.