Stabilisation of nonlinear systems using weighted angular method

The stabilisation of a class of nonlinear systems is studied using the angular form of a differential equation to reduce the problem to the control of the radial component of the state. In this method, the system is converted into two subsystems: one is a nonlinear equation on a sphere and the other is a radial differential equation. A stabilising control can be designed based on the one-dimensional radial system dynamics. The radial control may be continuous or discontinuous depending on the structure of the input map. Whenever the input map of the radial subsystem is zero, the radial control is not accessible. A method is presented to remove this obstacle. The control is designed using an appropriate weighting function.