A Fuzzy Framework for Managing Supply Chain Disruptions and Uncertainties via Aperiodic Time-Dependent Nonfragile Sampled-Data Control With Communication Delays

This article investigates fuzzy frameworks for analyzing the stability and stabilization of nonlinear supply chain systems (SCSs) affected by external disturbances and uncertainties. First, the dynamics of nonlinear SCSs are transformed into linear subsystems through Takagi-Sugeno (T-S) fuzzy frameworks. Then, the time-dependent nonfragile sampled-data controller (NSDC) with communication delays is developed to mitigate parametric uncertainties and attenuate external disturbances via $H_{\infty }$ -control theory. In contrast to existing NSDC methods, the constructed NSDC signals vary over time within each sampling period, thereby enhancing robustness and control performance. Thereafter, a novel integral inequality is developed to estimate the integral quadratic terms, where free-weighting matrices are uniquely assigned for each sampling stage and can take distinct values for different aperiodic sampling periods. To further reduce conservatism, an augmented dual looped-type Lyapunov functional (ADLLF) is introduced to fully utilize the knowledge of the aperiodic sampling pattern and communication delay effects. Subsequently, by leveraging this ADLLF along with the proposed integral inequality, sufficient conditions are derived as linear matrix inequalities (LMIs) to ensure the robust asymptotic stability of the T-S fuzzy SCSs with $H_{\infty }$ -performance level $\bar {\gamma }$ . Finally, the performance of the considered SCSs is validated through numerical simulations, and a comparative example demonstrates the effectiveness and superiority of the proposed theoretical findings.