Control Lyapunov Functions: New Framework for Nonlinear Controller Design

Control Lyapunov function (CLF) is a successful attempt to directly use of the Lyapunov function stability analysis technique of nonlinear systems in the synthesis problem. In this paper, on the basis of Freeman’s work (1996), the concept of CLF are re-analyze through using the method of set-valued analysis. And then, a new CLF based nonlinear controller design framework, called generalized pointwise min-norm (GPMN), is proposed. Simultaneously, three robust GPMN controllers are introduced with respect to respectively parameter uncertainties, external disturbance, and the combining cases. Actually, the framework provides us a new idea of nonlinear controller design since within which many other controller design indexes can be combined without re-considering the closed loop stability. Finally, a simple simulation is conducted to show one of the typical applications.