Sliding Mode Using Discontinuous Control Algorithms of Integral Type

This paper deals with the robust stabilization of continuous-time dynamical systems in the presence of parametric and external time-varying disturbances. Modified Variable Structure control algorithms with additional integral terms are considered here and analyzed. A comparison with a typical ``static'' VS algorithm is made. Static VS algorithms can reject completely the disturbance only if the amplitude of the switching term, in the control input, is larger than the amplitude of the disturbance itself. This paper shows how it is possible, by adding an integral term in the VS control algorithm, to reach and remain in the sliding mode if the amplitude of the switching term is smaller than the amplitude of the disturbance. Some simulations supporting the theoretical results are reported and discussed.