Fuzzy control synthesis for large‐scale systems with weighted interconnections

Abstract

This study examines the stabilisation problem associated with a particular type of large‐scale system. This type of large‐scale system consists of several non‐linear subsystems, which are connected to each other via interconnections of variable weighting. Interconnections of variable weighting between two subsystems denote that the interaction strength between the two subsystems is variable. Moreover, the weight may even be zero at some times or in some cases. In this study the authors suppose that the range of weight variation between any two subsystems is known, and that the stabilisation conditions for the large‐scale system are derived and that decentralised controllers which satisfy the conditions are synthesised. In the main result derivation, the Takagi–Sugeno ( T – S ) fuzzy model of a large‐scale system is used and a parallel distribution compensation (PDC) type fuzzy controller is synthesised based on the linear‐matrix‐inequality (LMI) method. Finally, a numerical example is given to demonstrate that the main theorem is applicable and the synthesised controller is effective.