An integral extension technique for continuous homogeneous state‐feedback control laws preserving nominal performance

This paper proposes a technique to extend a nominal homogeneous state‐feedback control law by continuous or discontinuous integral terms. Compared to pure state feedback, this permits to suppress non‐vanishing perturbations that are either constant or Lipschitz continuous with respect to time. The proposed technique seeks to do this while maintaining nominal performance in the sense that the nominal control signal and closed‐loop behavior is not modified in the unperturbed case. The class of controllers thus obtained is shown to include the well‐known super‐twisting algorithm as a special case. Simulations comparing the technique to other approaches demonstrate its intuitive tuning and show a performance preserving effect also in the perturbed case.