This article deals with the stabilisation of a ball on an actuated beam independently of whether or not the force acts on the non-actuated coordinate. The feedback control law is deduced via application of the traditional Lyapunov stability method. The balancing strategy consists of shaping a convenient energy function that allows us to derive the required asymptotic stabilising controller. To this end, we introduce an auxiliary control input variable in order to algebraically obtain the kinetic metric and the potential energy of the entire system. The formed positive energy function along with the proposed feedback controller assures that the overall system is a dissipative one.
['Carlos Aguilar-Ibanez']
The Lyapunov direct method for the stabilisation of the ball on the actuated beam