I have the following problem: in a continuous time control system, I
have proved
that a sliding mode can be enforced by using a relay control. I would
like
to show that if the command is sampled and held, the behavior of the
discrete time system "converges" to the continuous one when the
sampling
time goes to zero. This is somehow related to show that there exists a
regularization method for sliding mode control based on sampling the
discontinuous control law (instead of using a relay with small
hysteresis
or a saturation with high gain to approximate the discontinuous
element, as
Utkin does in his papers).
Is there anyone who can suggest me some bibliographic references
related to
this problem ? Many thanks (I apologize if I wasn't clear in the
explanation
of the problem).