Asymptotic stability of model reference systems with bang-bang control

The use of Lyapunov functions in the design of a fixed controller for model reference systems results in a bang-bang control. The motion in the neighborhood of the switching surface is analyzed and conditions are found that ensure stable trajectories. It is shown that the Lyapunov design verifies these conditions. The last part of the trajectories appears to be a sliding motion, forcing the plant to track the model. The results are illustrated by a simulation example.