State difference feedback for stabilizing uncertain steady states of non-linear systems

Supposing a non-linear system is subjected to parametric uncertainties, the present paper aims at stabilizing its unstable steady states. A distinctive feature of the problem is that exact information about the steady state is unavailable. To cope with the difficulty, we have examined the applicability of the state difference feedback which uses the difference between the present state x(t) and the past state x(t - T). A rigorous stability analysis has been executed for the case where state deviations are controllable by a single input variable. The stability analysis has led to a favourable conclusion that if the number of unstable modes is just two, and if they are not associated with the origin in the complex plane, we are always able to rnd a controller which stabilizes the deviations from the unknown steady state. Design process is illustrated by using two kinds of pendulum systems.