Variable structure control of single time-delay discrete singular uncertain system

Synthesis and designing of variable structure controller for linear discrete uncertain time-delay singular system are 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, based on some results on asymptotic stability of discrete time-delay singular systems, a switching function with difference compensator is designed, which guarantee the system is asymptotically stable in quasi-switching manifold. Thirdly, different variable structure controllers are designed respectively in terms of two cases that the uncertain part is bounded and the uncertain part changes slowly. The controllers 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.