Variable structure control of linear time-delay uncertain singular system

Synthesis and designing of variable structure controller for time-delay singular uncertain system are studied. Firstly, the system is decomposed into two low dimensional subsystems. Secondly, switching function and variable structure controller are designed with regard to uncertain part of the system satisfies matching conditions or not. The designing guarantee the movement of the system in switching manifolds is asymptotically stable and the variable structure controller can force trajectory of the system to arrive at the switching manifold in finite time. Finally, a numerical example and its simulation figure are given to demonstrate feasibility and validity of the design method.