Robust Stabilization of Singular Systems Including State Delay via Sliding Mode Control

The present paper concerns with the sliding mode control for uncertain singular time-delay systems. First, a proportional-integral switching surface is newly proposed such that the sliding mode motion is not only asymptotically stable but also with a prospective stability degree. This type of switching surface does not allow for a reduction of order as it is the case with most sliding mode control. This property of switching surface make it easy to design a sliding mode controller for the considered singular time-delay systems. Then based on the switching surface, a sliding mode controller is derived to guarantee the occurrence of sliding mode motion in finite time. Finally, a numerical example is given to show the design procedures.