A guiding function approach to stabilisation of a class of nonlinear systems

In this paper we present a very simple yet effective approach to the construction of piecewise constant feedback stabilization strategies for a class of nonlinear systems without drift in which the difference between the number of state and control variables is equal to one. The approach exploits a set of guiding functions whose number is equal to the number of the controls in the system. The guiding functions are chosen in such a way as to permit a sequence of controls which results in a monotonic decrease in one of the guiding functions while the remaining ones are varying in an oscillatory way