Discontinuous feedback stabilization of a hopping robot in flight phase

A systematic approach to the construction of feedback control for set point stabilization is presented for a model of a hopping robot in flight phase. The feedback controls are piece-wise constant and the method relies on the construction of a Lyapunov function. This Lyapunov function is a sum of two semi-positive definite functions, which are determined by using Lie algebraic methods and Frobenius theorem. The constructed Lyapunov function decreases in an average sense.