This study addresses the stability and stabilization challenges in nonlinear control systems with time-varying delays via fuzzy model theory. An exponentially narrow delay interval technique is introduced, facilitated by a single tunable parameter p, to equivalently transform the extensive delay period \([d_0, d_2]\) into a series of variable narrow subintervals, expressed as: \([d_{0},d_{2}]=\cup _{i=1}^{2^l}[d_{\frac{i-1}{2^{l-1}}},d_{\frac{i}{2^{l-1}}}]\) . Diverging from traditional delay interval methods, this narrow delay interval approach simplifies the optimization process by characterizing each subinterval with just \(d_0\) , \(d_2\) , and p. The core advantage of integrating the narrow interval approach with fuzzy systems is its capability to accurately represent and manage the intrinsic uncertainty in time-varying delays, thus facilitating robust control in real-world scenarios. A parameter-type reciprocally convex inequality is introduced to estimate the derivative of the narrow Lyapunov-Krasovskii functional, enhancing the precision over conventional methods. These innovations contribute to the formulation of new criteria for the stability and stabilization of the T-S fuzzy delayed system. The practicality and effectiveness of the proposed strategies are demonstrated through their application to a truck-trailer system.
