Output Feedback Discontinuous Integral Controller for SISO Nonlinear Systems

In this paper we provide a homogeneous integral control by output feedback which is able to stabilize in Finite Time the origin of a SISO nonlinear system and reject matched Lipschitz perturbations. For the system in normal form, we construct a homogeneous Lyapunov function, that proves the stability of the closed loop system combining a state feedback discontinuous integral controller and a smooth state observer. We present the results for systems with relative degrees 2 and 3, although the developed Lyapunov based analysis and design method can be extended to the arbitrary relative degree case. Moreover, in contrast to previous works, the signal to be fed to the integral controller can be a fairly arbitrary function of the states.