Robust Control Designed by Composition of Lyapunov Functions

A new method of designing a robust control law is proposed for a general class of nonlinear or linear systems with bounded uncertainties. The method uses the property that the Lyapunov function is not unique for a stable or stabilizable system. It is shown that the proposed control law normally guarantees the stability of the system if there are two Lyapunov functions whose null sets have a trivial intersection. The results require no knowledge about the structure and size of the input-unrelated uncertainties. Moreover, it is shown that asymptotic stabilisation of the nominal system is not necessarily required in this method.