Sliding Mode Control of Uncertain Time Delay System using Lambert W Function

This paper presents a robust sliding mode control law for time delay systems with parametric uncertainties and external disturbances. The uncertainties and disturbances are assumed to be matched. The method for designing a switching hyperplane using Lambert W function is proposed for generation of sliding motion in the system. This method includes desired eigenvalue placement for getting a stable sliding manifold. A controller is designed such that system trajectories reach sliding surface in finite time and remain there for all subsequent time. Simulation results are also shown on a numerical example to illustrate the effectiveness of the proposed method.