A singular perturbation approach to sliding mode control in the presence of input delay

It is well known that arbitrary small delays in the sliding mode control lead to oscillations and the systems may even become unstable for a greater values of the delay. Output feedback sliding mode control of systems with bounded matched disturbances is considered under small time-varying input delay, which is unavoidable in the feedback. The design objective is to achieve ultimate boundedness of the closed-loop system with the bound proportional to the delay and to the disturbance bounds. Sliding mode controller with a high linear gain is proposed, which leads to the closed-loop singularly perturbed system. An LMI-based solution for evaluation of the design parameters and of the resulting ultimate bound is derived by using different Lyapunov-based methods.