Synthesis of variable structure controller for time-delay uncertain singular system

Synthesis and design of variable structure controller for time-invariant linear time-delay singular system is studied. Firstly, a new restricted system equivalent form is developed. In the case that uncertain part of the system satisfy matching conditions, the system is decomposed into two low dimensional subsystems: one is a normal linear differential difference system without input; another is a linear difference system with uncertain party and input. Secondly, based on some results on asymptotic stability of singular system with time-delay, switching function with integral compensator is studied, and sufficient conditions on asymptotic stability of sliding mode are given. Thirdly, variable structure controller is designed, which can force the solution trajectory of the system to arrive at slide manifold in finite time. Finally, two numerical examples are given to demonstrate feasibility and simplicity of the design method.