Higher order super-twisting algorithm

Generalization of the Super-Twisting algorithm (STA) for r relative degree system with respect to output, ensuring finite time convergence to the set σ, σ̇,..., π^(r) where σ represents the output via absolutely continuous control signal using information of σ, σ̇,..., π^(r)-1 are discussed. The convergence conditions for the 3-STA algorithm are proposed. The formula for algorithm of arbitrary order is suggested. The simulations results are confirmed the efficiency of the proposed algorithm.