Stabilisation of multi-input nonlinear systems using associated angular approach

In this paper the stabilisation of multi-input nonlinear systems is studied using the associated angular approach. In this method, a nonlinear system is converted into two associated subsystems, the so-called radial and spherical subsystems. For a single input nonlinear system, the control is designed using the one dimensional radial system to stabilise the radial and consequently the original nonlinear system. For multi-input systems, the control is also designed based on the radial subsystem, however, the method is not straightforward in comparison with single input systems. The control law includes a weighting function which is determined based on the system performance and control action. Some examples are presented to illustrate the effect of various scenarios of using the proposed method.