Acrobot Stable Walking in Hybrid Systems Notation

The Acrobot walking is interesting and still challenging control problem. By virtue of an actuator location, the Acrobot is partially feedback linearizable up to order 3. This property is widely used both in a feedback tracking of a reference trajectory and in the reference trajectory design. Moreover, the walking of the Acrobot consists of continuous-time and discrete-time dynamics, therefore, the Acrobot belongs in a class of hybrid systems. The aim of this paper is to integrate continuous-time and discrete-time dynamics into a general model of hybrid systems and prove hybrid stability of the Acrobot walking by using both the already developed feedback control and the reference multi-step trajectory.