Practical Fixed-Time Synchronization of T–S Fuzzy Complex Networks With Different Dimensions

This paper studies the practical fixed-time synchronization control of T-S fuzzy complex networks with different dimensions, a topic for which no prior solutions exist, despite extensive research on the synchronization of T-S fuzzy complex networks with the same dimensions. First of all, under the semi-intermittent framework, by adopting a more relaxed average control rate under the new definition, a novel fixed-time stability lemma with a unified exponential condition is established, which can reduce the input of parameters irrelevant to the system. Considering the important practical application significance of the practical fixed-time stability, two new practical fixed-time stability lemmas are further obtained based on two different algorithms, which can greatly improve the existing ones. By using the transformation of the same dimension, some new results on the practical fixed-time synchronization control of the considered networks are given by designing the intermittent event-triggered controllers with exponential gains, which have smaller trigger frequency and higher trigger efficiency than the traditional event-triggered controllers. In parallel, both static and dynamic event-triggered controls have been designed, and the dynamic function has been stringently proven to be positive via simple conditions. This accomplishment addresses a long-standing issue in the extant literature, where the presence of high-order terms in the dynamic function had hitherto precluded or failed to establish its non-negativity. Finally, the viability of the acquired results is demonstrated through numerical simulations.