Variable structure control for uncertain discrete singular system with structured perturbation and time-delay

The variable structure control problems for a class of time-delay discrete uncertain singular systems with structured perturbation were studied. A new switching function with a difference compensator is designed, which guarantees that movement of the system is asymptotically stable in a quasi-switching manifold, then a variable structure controller is designed, which can force the system trajectory to enter into a small neighborhood of the quasi-switching manifold in limited steps and be convergent to a small chattering in the neighborhood. Finally, a numerical example was given to demonstrate the effectiveness and practicability of the design method.