Robust Stabilization and ℒ₂-Gain Sensitivity Specification for Nonlinear Systems with Stable Zero Dynamics and Matched Uncertainties

The exact feedback linearization technique with partial state feedback and stable zero dynamics ensures local exponential stability. However, the method requires an accurate model, without uncertainties. The paper proposes an extension of the method for input-affine nonlinear systems with stable zero dynamics and matched uncertainties. Moreover, the weighted closed-loop sensitivity function is imposed using the ℒ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf>-gain analysis. The advantage of the proposed extension is that it ensures both robust stability and performance (tailored to reference tracking) for the uncertain nonlinear system affected by the limitations of zero dynamics. The two methodologies are then illustrated on a given academic example.