Uniformly continuous differintegral sliding mode control of nonlinear systems subject to Hölder disturbances

An integral sliding mode controller based on fractional order differintegral operators is proposed. This controller generalizes the classical discontinuous (integer order) integral sliding mode scheme. By using differintegral operators, their topological properties lead to a uniformly continuous controller that enforces an integral sliding mode for any initial condition. In addition, it is demonstrated that the proposed scheme is robust against matched Hölder continuous, but not necessarily differentiable, disturbances and uncertainties. Also, asymptotic convergence of tracking errors is assured for any initial condition by means of an ideal controller, even in presence of anomalous but Hölder continuous disturbances. It is worth to mention that the salient properties of our proposal (i.e. invariance at any initial condition, uniform continuity, and robustness to non-differentiable disturbances) are not provided by any existing integer order sliding mode based controller of the literature. The viability of the proposed scheme is shown in a representative simulation study.