Sliding mode control design via Lyapunov approach

The paper discusses sliding mode control design for nonlinear dynamic systems by means of Lyapunov functions. The control objective is to stabilize the state to an equilibrium manifold. It is shown that there exist a linear hypersurface in control space which we call the decision manifold such that the control design goal is accomplished if at each time the value of control is chosen in an appropriate halfspace. Conditions are found when there exists a bounded control solving the problem. It is demonstrated how the classical variable structure control algorithms fit into this framework. The approach makes it possible to characterize a wide class of designs. An example of a ground vehicle automated steering control illustrates the technique