LAUSR

Abstract We 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 to Lipschitz (matched) perturbations, i.e. perturbations with bounded derivative; and (iii) providing a continuous control signal, and thus reducing the chattering effect of a discontinuous controller.