Dynamical Radial Control of Nonlinear Systems

This paper is concerned with the stabilisation of a general class of nonlinear systems via the associated angular approach. In this method, the system is converted into two subsystems the so called radial and spherical systems. The spherical system is a nonlinear equation on a sphere and the radial system is a scalar 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. In this paper a method is presented to remove this obstacle. The control is designed by including an extra dynamic to the system. Therefore the new system is an augmented system. The radial auxiliary input map of the augmented system i.e. the original control is the new state. Since it is assumed that the original control is not zero, the auxiliary radial control is definable within the operating region.