In this study, we present a novel fuzzy control strategy that considers the influence of lead times on nonlinear supply chain management (SCM) systems. The authors have constructed a fuzzy control model for an SCM model based on nonlinear phenomena with lead times, drawing inspiration from Takagi-Sugeno's (T-S) fuzzy control system. Additionally, the authors have designed a fuzzy H ∞ control approach to mitigate the effects of lead times, switch between sub-models, and address customers' stochastic requests, all while considering the concept of maximal overlapped rules groups. The control of nonlinear supply chain management is implemented in a manner that ensures asymptotic stability and facilitates smooth transitions from one subsystem to another. The introduction of the membership function into the fuzzy system results in reduced fluctuations in the system's variables. The key contributions of the research include the design of a fuzzy H ∞ control approach, leveraging maximal overlapping-rules group (MRRG) to ensure stability through localized definite positive matrices identification. This strategy achieves two primary objectives: asymptotic stability of the supply chain system and smooth switching between nonlinear SCM elements. The authors demonstrate the effectiveness of their proposed method through comprehensive comparisons with the fuzzy H ∞ control technique. The study provides a valuable insight into managing lead times in SCM through dynamic and stable control methodologies. Finally, a comprehensive comparison is provided between the suggested H ∞ management approach and the fuzzy H ∞ control strategy. This comparison is demonstrated through two-stage nonlinear numerical simulations, keeping SCM lead times in mind. Movement results are presented to illustrate the effectiveness of our suggested algorithm. • A fuzzy control for mitigating the effects of lead times. • Considering stochastic demands from customers. • MRRG in T-S fuzzy system linked to control ensures stability. • Proposed control ensures smooth switching in nonlinear supply chain elements. • Linked to fuzzy H_∞ control, our method is paralleled for effective demonstration. [ABSTRACT FROM AUTHOR]