Robust stabilisation of linear time-invariant time-delay systems via first order and super-twisting sliding mode controllers

This study presents a novel scheme for the synthesis of first-order and super-twisting sliding mode controllers for the robust stabilisation of a class of linear time-invariant time-delay systems subject to matched disturbances. Starting from a stability analysis of the system to guarantee that the resulting sliding mode dynamics is asymptotically stable, linear matrix inequality conditions of reduced conservatism are derived by using the Lyapunov-Krasovskii approach. Based on the stability analysis, the sliding mode controllers are synthesised to force the evolution of the closed-loop system trajectories to converge onto a prescribed sliding surface and to ensure that they remain there for all subsequent time. Unlike existing results, the implementation of the proposed approach does not involve strong requirements on the system structure. A numerical and a practical example along with a comparative analysis prove the effectiveness of the proposal and highlight its benefits.