Synthesis and design of variable structure controller for linear discrete uncertain multiple time-delays 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; another is a difference system with input. Secondly, based on the above decomposition and some results on Robust stability of discrete time-delay singular systems, a switching function with difference compensator is designed, which guarantees the movement of the system is asymptotically stable in quasi-switching manifold. Thirdly, under assumption that the uncertain part is bounded, a variable structure controller is designed, which can force solution trajectory of the system either to arrive at the quasi-switching manifold in finite steps and ultimately slide to zero on the quasi-switching manifold or to enter into a small neighborhood of the quasi-switching manifold in finite steps and stablly convergent to a small chattering in the neighborhood. Finally, a numerical example is given to demonstrate feasibility and simplicity of the design method.
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