Robust sliding mode control of uncertain second order system with single unknown time variable control coefficient

The situation of second order system with single time variable control coefficient and uncertain model parameters is controlled with an robust sliding mode controller since adaptive method is improper to cope with the situation that control coefficient is not a constant. What is worthy pointing out is that four kinds of situation are discussed and whether bounded gain is possible for the controller to make the system stable is depended on the variable control coefficient is increasing or decreasing. At last, detailed simulation was done to testify the rightness of the proposed method.