Robust stabilization of internally delayed uncertain systems via sliding mode control (Q1919102)

A control system with delay is considered in the presence of bounded parametric uncertainties. Under suitable assumptions, the existence of a sliding motion of this system (by using a state feedback control) is established. Sufficient conditions, ensuring robustness of the system with respect to the uncertainties when a suitable sliding motion is generated, are proved. A method to design a switching hyperplane to guarantee asymptotic stability of the system, is suggested. In the case when an ideal relay device (under unity feedback) is used, a way to eliminate limit cycles is proposed. For a particular choice of this control system, it is shown that the obtained results are simple to use in design and implementation. Some simulation results are presented.