SMC of Uncertain Linear Discrete Time Systems with Input Delay

Abstract

Many papers have considered the problem of SMC for classes of uncertain systems with time-delay [161, 147, 189, 160, 10, 8, 9]. Although much attention has been given to the control problem of discrete systems with time-delay [96, 127, 168, 154, 51], few results have been reported on robust control of systems with time-delay in discrete time with discrete SMC.

A discrete version of SMC is important when the implementation of the control is realized digitally using a relatively slow sampling period. It is worth pointing out that discrete sliding mode control cannot be obtained from their continuous counterpart by means of simple equivalence. In [34], the problem of discrete Variable Structure Control (VSC) was first considered. The concept of the quasi-sliding mode was suggested in [134], and phenomena of switching, reaching, and quasi-sliding mode were investigated in [55].