In this paper, discretization effects on the dynamical behaviors of equivalent control based multi-input sliding-mode control systems is studied. Boundary conditions for the system steady states are established. Furthermore, properties of asymptotically convergent periodic trajectories are characterized by using new concepts of symbolic vector and symbolic vector sequence. Finally, the theoretical results are verified through the simulation study of a third-order system with two inputs.
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Yu et al. (2008) studied this question.