HOSM Output feedback control of uncertain SISO linear plants

We propose an output feedback High-Order Sliding Mode (HOSM) controller for a class of uncertain SISO Linear Time Invariant systems. It is able to nullify the output of the system globally and in finite-time, despite of the uncertainty in the (constant) coefficients of the system and in presence of matched non-vanishing perturbations, that can grow linearly with the state of the system. This improves the possibilities of the classical High-Order Sliding Mode controllers, which are not able to deal globally with linear system’s vector fields. The result is obtained by using control laws and injection terms of observers composed of classical linear terms and the homogeneous terms of the classical HOSM. The stability of the closed-loop dynamics is proved using non-homogenous explicit Lyapunov functions. The results are illustrated by some simulations.