Convergent adaptive control based prescribed-time synchronization of switched fuzzy competitive network systems with time-varying delays.

This paper addresses the prescribed-time control problem for discontinuous fuzzy neutral-type competitive neural networks (FNTCNNs) featuring switchings and time-varying delays. Notably, FNTCNNs constitute a generalized class of singularly perturbed Filippov systems. The establishment of a prescribed-time stability lemma for time-varying delay singularly perturbed systems remains a critical yet unresolved challenge. To address this, we first develop a novel prescribed-time stability lemma for singularly perturbed Filippov systems using adjustment functions, the comparison principle, and inequality techniques. This is achieved through the application of the one-norm and the introduction of a new stability definition for such systems. Considering the switching law inherent in FNTCNNs, we achieve prescribed-time stabilization control by designing adaptive prescribed-time control strategies, employing differential inclusion theory and Filippov's solution framework. The proposed adaptive control strategies demonstrate convergence properties, ensuring that both the control strategies and system state variables converge to zero within the same prescribed-time interval. These newly developed strategies offer significant advantages over existing approaches. Finally, we validate our principal results through numerical simulations of second-order multi-agent systems subject to discontinuous disturbances.