Asymptotic stability and sampled data control of hybrid nanofluid in a time-delay nonlinear Brinkman system

Our approach in the present work is concerned with a novel study involving a sampled-data controller for hybrid nanofluid in a time-delay nonlinear Brinkman system with randomly occurring uncertainties. The time-delay error system is described by utilising a hybrid nanofluid in nonlinear system and the looped Lyapunov–Krasovskii functional with a splitting sampling interval. In order to ensure that the resulting closed-loop system is reliable, it is asymptotically stable and has the required dissipative efficiency. A master/slave synchronisation technique is employed to synchronise the hybrid nanofluid in nonlinear system. In addition, we employed a sampling interval \([t_{k}, t_{k+1}]\) and the fractional parameter \({\tilde{\beta }}\) in the interval [0,1] has split into \([t_{k}, t_{k} +{\tilde{\beta }} \varsigma _{1}(t)], [ t_{k} +{\tilde{\beta }} \varsigma _{1}(t), t], [t, t +{\tilde{\beta }} \varsigma _{2}(t)]\) and \( [ t +{\tilde{\beta }} \varsigma _{2}(t), t_{k+1}]\). Then, the synchronised hybrid system utilises the looped Lyapunov stability theory and positive definite matrix. The simulation results not only confirm the theoretical predictions but also demonstrate enhanced control performance, improved synchronisation accuracy and robust dynamic stability. Furthermore, this study highlights the impact of time-delay, uncertainty and fractional parameter variations on system stability. The proposed approach provides a new direction for advanced control strategies in nanofluid-based nonlinear systems, offering potential applications in engineering and industrial processes. Finally, certain simulation results verify the effectiveness and correctness of the analytical results.