LMI based design for the Acrobot walking

This paper aims to further improve previously developed design for Acrobot walking based on partial exact feedback linearization of order 3. Namely, such an exact system transformation leads to an almost linear system where error dynamics along trajectory to be tracked is a 4-dimensional linear time-varying system having 3 time-varying entries only, the remaining entries being either zero or one. In such a way, exponentially stable tracking can be obtained by quadratically stabilizing a linear system with polytopic uncertainty. The current improvement is based on applying LMI methods to solve this problem numerically. This careful analysis significantly improves previously known approaches. Numerical simulations of Acrobot walking based on the above mentioned LMI design are demonstrated as well.