Output feedback in variable structure systems with a simple adaption law

This note proposes an output feedback variable structure control to stabilize a class of uncertain systems, in which the states are unavailable and the upper bounds of uncertainties are unknown. Under a certain condition, the sliding (switching) hyperplanes are chosen to stabilize the reduced order equivalent system in the sliding mode. Further, based on an improved Lyapunov function, the controller gain is obtained by a simple adaptation law without any knowledge of the system dynamics such that the stability of the sliding mode is ensured. Finally, a practical aircraft model is given to illustrate this design approach