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The primary objective of this thesis is to present that the
sliding control can be transformed as a frequency-domain Lur''e
problem and to eliminate the chattering phenomenon. The
traditional sliding mode is often performed by the state space
approach. In the formulation, it is shown that with the
classical nonlinear sign function,the sliding mode control can
only quarantee the overall system stable but not asymptotically
stable. We prove that if thenonlinear sign function contains a
hysteresis loop,even it is very small,there will exist ahigh
frequency and small amplitude limit cycle. This coincides theso-
called "chattering phenomenon" in the sliding mode control.
In the conventional sliding mode control, the relative degree of
the chosensliding surface is usually one. This paper addresses a
general class of slidingsurface whose relative degree is no-
longer restricted to one. We show that whenthe relative degree
is more than two,it is inevitable that there exists a limitcycle
for the nonlinear sign function.Even in the case of relative
degree two,the system reveals zero degree phase margin. However,
these disadvantages can be remedied by introducing a suitable
boundary layer width for the nonlinear saturation function that
ensures global,exponential stability of the overall system.
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