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In control system design, it is often required that the
system behavior is insensitive to the parameter variations and
external disturbances. To this problem, variable structure
system control is developed and widely applied. Traditional
sliding mode control possesses the characteristics that the
controlled system is invariant to model uncertainty and external
disturbance when the state enters the sliding surface, and the
system response follows the dynamics of the sliding surface.
However, when the sliding mode controller is realized by digital
computer, it is impossible for the control input to switch in a
very high frequency and the sliding mode motion will not
occurred. The respective robustness vanishes, and the system
may become unstable when the sampling period is too long.
In this dissertation, a discrete-time sliding control law, which
is applied immediately after sensing the system states, is
developed to guarantee the existence of the weak-pseudo-sliding
mode along the prescribed hyperplane. Due to the effect of the
computational delay, an one-sample-delay discrete-time sliding
mode control law is developed. Concept of the "modified weak-
pseudo-sliding mode" is proposed. The upper bounds of the
sampling periods are also determined to ensure the stability.
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