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).
- posted
18 years ago