Stability robustness to unstructured uncertainty for nonlinear systems under feedback linearization

This paper addresses robustness to linear unstructured uncertainty at the plant input for MIMO nonlinear systems under feedback linearization. For simplicity, the plant is assumed to be exact feedback linearizable and in the so-called normal form. Two sufficient conditions for BIBO stability in L₂ are given, under respective assumptions on the nonlinear dynamics of the nominal plant, using a small gain argument. The first condition applies to general exact feedback linearizable nonlinear plants in normal form, but is shown to be too conservative for practical use. The second condition is shown to be practical and analogous to well known stability robustness results for LTI systems. In particular, it has a simple frequency domain interpretation and embodies the loop-shaping concept of the LTI result. However, this result can only be applied to a restricted class of nonlinear plants. Therefore, the two results of this paper can be viewed as two extremes in terms of practicality and generality in which there is a tradeoff between these two qualities