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 against some classes of uncertainties and disturbances. However, this control produces chattering which can cause instability due to unmodeled dynamics and can also cause damage to actuators or the plant. There are essentially two 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 switching surface and use continuous control inside the boundary. The problem with 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 observe that variable. In the second method, it is important that the trajectories inside the boundary layer do not try to come outside the boundary after entering the boundary layer. Control laws producing chattering-free sliding mode using a boundary layer have been proposed and the existence of solutions to the system using these control laws are presented