Variable structure control of time-variant linear time-delay singular system

Synthesis and designing of variable structure controller for time-variant linear time-delay singular system is studied. Firstly, a new restricted system equivalent form is developed and the system is decomposed into two low dimensional subsystems. Secondly, switching function with integral compensator is designed and sufficient conditions on asymptotic stability of the sliding mode are given. Thirdly, variable structure controller is designed, which guarantee the solution trajectory of the system arrive at the slide manifold in finite time. Finally, a numerical example is given to demonstrate feasibility and simplicity of the design method.