Practical and Exponential Stabilization of Takagi–Sugeno Fuzzy Systems Under Unknown Time‐Varying Delays

This article addresses the practical and exponential stabilization of Takagi–Sugeno (T–S) fuzzy systems subject to unknown time‐varying delays and heterogeneous perturbations. Two state‐feedback controllers are proposed: a practical stabilizer that drives the trajectories into a prescribed residual set and an exponential stabilizer that ensures convergence to the origin. The design is based on subsystem‐specific delay‐compensation terms and a common quadratic Lyapunov function. Sufficient stability conditions are derived in the form of linear matrix inequalities (LMIs), explicitly accounting for fuzzy blending and region‐dependent perturbations. The proposed approach extends delay‐compensation ideas from the single‐model nonlinear setting to the T–S fuzzy framework. Numerical examples involving an inverted pendulum, a nonlinear mass‐spring‐damper system, and a DC motor demonstrate the effectiveness and robustness of the proposed controllers.