Generalized Point Wise Min-Norm Control Based on Control Lyapunov Functions

A new nonlinear controller design method based on control Lyapunov functions, called generalized point wise min-norm controller, is presented in this paper, which is a generalized version of Freeman´s point wise min-norm controller in 1996. And the continuity of the new controller is proved using the set valued analysis theory. The greatest improvement of the new controller, comparing with the Freeman´s controller, is its greatly improved designing flexibility from the induced guide function. And it is shown that the new control method can be used together with some other controller design method with special performance index by the concept of guide function, especially those that the closed loop stability cannot be ensured sufficiently. Finally, an example is given combining with a linearized controller to both enlarge the large scale stability and preserve the local performance of that.