High-order sliding-mode observer–based input-output linearization

The problem of output control in multiple-input–multiple-output nonlinear systems is addressed. A high-order sliding-mode observer is used to estimate the states of the system and identify the discrepancy between the nominal model and the real plant. The exact and finite-time estimation may be tackled as long as the system presents the algebraic strong observability property. Thus, a continuous robust input-output linearization strategy can be obtained with respect to a prescribed output. As a consequence, the closed-loop dynamics performs robustly to uncertainties/perturbations. To illustrate the advantages of the proposed method, we introduce a study case that demands a robust linear system behavior: the self-oscillations induced in an underactuated mechanical system through a two-relay controller. Experiments with an inertial wheel pendulum illustrate the feasibility of the proposed approach.