摘要：AbstractWe propose a homogeneous integral controller with positive homogeneity degree, for systems with relative degree two and three. Its design and the convergence proof is achieved by the construction of an explicit homogenous Lyapunov function. A combination of this controller, with a discontinuous one developed by the authors in a previous work, allows to achieve: (i)fixed time convergence,that is that the maximal convergence time is a constant independent of the size of the initial conditions; (ii) insensitivity toLipschitz (matched) perturbations,i.e. perturbations with bounded derivative; and (iii) providing acontinuous control signal,and thus reducing the chattering effect of a discontinuous controller.
关键词：KeywordsLyapunov functionsHomogeneityHigher Order Sliding modesOutput TrackingIntegral Control
