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• This paper deals with designing fuzzy PDC controllers for nonlinear neutral time-delay systems with impulsive effects. • The proposed approach employs system augmentation, ITD Lyapunov functions, and a dilated LMIs technique. • Two LMI-based conditions for the existence of fuzzy PDC controllers are presented. The state feedback fuzzy controller synthesis for nonlinear neutral state-delayed systems with impulsive effects is addressed. A methodology for stability analysis of the underlying systems is proposed in the framework of system augmentation. New impulse-timer-dependent Lyapunov functions based analysis techniques, including a Razumikhin-type technique and a Lyapunov functional technique, are developed allowing to reduce the conservativeness of the stability conditions. To circumvent the difficulty in designing control gain matrices, the stability conditions of the closed-loop system are formulated in terms of dilated linear matrix inequalities (LMIs). By virtue of the nice properties of the dilated LMIs, the fuzzy controller synthesis is established. Three illustrative examples are presented to demonstrate the novelty of the new stability criteria and the effectiveness of the proposed design method. [ABSTRACT FROM AUTHOR]

• New analysis and design methods based on the use of impulse-time-dependent Lyapunov function/functional are proposed. • The restrictive condition on the relationship between the size of time-delay and lower bound of impulse intervals imposed by the previous results is removed. • The fuzzy PDC control design methodology for both cases of fast and slow time-varying delay is developed. This paper is concerned with robust stabilization problem of Takagi–Sugeno (T-S) fuzzy time-delay systems subject to impulsive perturbations. New results on robust stabilization via parallel distributed compensation (PDC) control are derived. First, based on the impulse-type Razumikhin–Lyapunov method combined with the use of an impulse-time-dependent Lyapunov function, a new exponential stability criterion for T-S fuzzy time-delay system with impulsive effects is obtained. The proposed stability criterion removes the restrictive condition on the relationship between the size of time-delay and lower bound of impulse intervals imposed by the previous results. Then, by employing a convex relaxation technique, a sufficient condition for the constructing the PDC controllers is presented, which is expressed in terms of linear matrix inequalities (LMIs). Next, the robust stabilization problem for the T-S system with slowly time-varying delay is studied. A different stabilization condition is derived via an impulse-time-dependent Lyapunov functional, which is less conservative than the former when the state delay is constant. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed analysis and design techniques. [ABSTRACT FROM AUTHOR]