Quasi-sliding mode variable structure control of time-delay discrete singular uncertain system

Designing of sliding mode variable structure controller for linear discrete uncertain 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: one is a difference system without input; the other is a difference system with input. Secondly, under assumption that structural perturbation matrices are bounded, switching function with difference compensator is designed, which guarantee the system is asymptotically stable in quasi-switching manifold. Thirdly, sliding mode variable structure controller is designed, which can force solution trajectory of the system to enter into a small neighborhood of the quasi-switching manifold in finite steps and to converge to a small chattering in the neighborhood ultimately. Finally, a numerical example is given to demonstrate feasibility and simplicity of the design method.