Exponential stabilization of time-varying delay systems with non-linear perturbations

This paper provides a linear matrix inequality (LMI)-based approach for exponential stabilization of time-varying delay systems subject to either non-linear perturbations or parametric perturbations. The time-varying delay varies within an interval with known lower and upper bounds. Its time derivatives can be known or unknown. By choosing a set of improved Lyapunov–Krasovskii functionals that includes triple-integral terms, delay-dependent stabilizability conditions involving lower and upper delay bounds are derived to ensure closed-loop stability of the system with any prescribed α-convergence rate. The design of memoryless state feedback controllers can be carried out in a systematic and computationally efficient manner via the use of LMI-based algorithms. Extensive numerical examples are given to demonstrate the effectiveness of the proposed design method and its improvement over some existing results in the literature.