Multivariable variable-gain super-twisting control via output feedback for systems with arbitrary relative degrees

An output-feedback super-twisting algorithm (STA) with variable gains is developed for multiple-input and multiple-output plants with arbitrary relative degrees. Global or semi-global finite-time exact tracking can be guaranteed for a class of uncertain systems with matched nonlinear time-varying disturbances, possibly dependent on the unmeasured states. This represents a significant generalization of recently introduced versions of the STAs to a multivariable setup with arbitrary relative degrees, output-feedback, and variable gains. The construction of such controller is based on a higher-order sliding-mode multivariable differentiator with dynamic gains. The gain adaptation for the controller and differentiator employs state-norm observers to overcome the lack of the full-state measurement. The stability properties of the proposed control system are demonstrated by means of input-to-state stability tools and a Lyapunov function-based analysis. The theoretical results are verified through numerical and academic examples.