Existence of solutions to a class of nonlinear convergent chattering-free sliding mode control systems

Sliding mode control is a nonlinear control technique, which is robust agai nst some classes of uncertainties and disturbances. However, this control p roduces chattering which can cause instability due to unmodeled dynamics an d can also cause damage to actuators or the plant. There are essentially tw o ways to counter the chattering phenomenon, One way is to use higher order sliding mode, and the other way is to add a boundary layer around the swit ching surface and use continuous control inside the boundary, The problem w ith the first method is that the derivative of a certain state variable is not available for measurement, and therefore methods have to be used to obs erve that variable. In the second method, it is important that the trajecto ries inside the boundary layer do not try to come outside the boundary afte r entering the boundary layer. Control laws producing chattering-free slidi ng mode using a boundary layer have been proposed and the existence of solu tions to the system using these control laws are presented in this paper.