H ∞ synchronisation of fractional-order clifford-valued reaction–diffusion neural networks with leakage delays via sampled-data control

This paper addresses the H∞ synchronisation of fractional-order Clifford-valued reaction–diffusion neural networks with leakage delays and sampled-data control. The study is motivated by spatially distributed neural and signal-processing systems in which each node carries several algebraically coupled channels, such as colour, polarisation, orientation, or sensor-fusion features. A Clifford-valued model treats these channels as a single hypercomplex state, while the fractional derivative describes long-memory behaviour, the reaction–diffusion term captures spatial propagation, and the leakage delay represents delayed self-inhibition. These features are therefore considered together because they arise simultaneously in networked digital implementations rather than as separate mathematical embellishments. For the drive-response error system, an L2 Lyapunov–Krasovskii functional is constructed by combining the current error energy with leakage- and coupling-delay integral terms. Green's formula, the Poincare inequality, the Caputo Lyapunov inequality, and a sampling-error estimate are used to derive explicit scalar conditions for Mittag–Leffler synchronisation. The sampling estimate is formulated in terms of a Caputo-Hoelder bound and is valid for every fractional order α∈(0,1), avoiding the singular restriction that occurs in estimates based on (2α−1)−1. The same framework yields an H∞ performance criterion with a prescribed disturbance-attenuation level and a closed-form upper bound for the allowable sampling interval. The numerical section includes two bounded simulations, a heterogeneous-network test, sampling and parameter sensitivity studies, benchmark comparisons, CPU-time reporting, and a detailed image-encryption validation. The figures show meaningful transient dynamics, non-zero synchronised drive-response trajectories, bounded control amplitudes, and no numerical overflow.