Stability robustness of feedback linearisable systems with input unmodelled dynamics

The stability robustness of a feedback linearisable system subject to unstructured uncertainty is studied, with respect to the concepts of local input-to-state stability (ISS), local input-to-output stability (IOS) and small-signal L-2-stability. PI nonlinear small-gain theorem for feedback interconnected systems that are characterised by both local ISS and IOS is established. This theorem is used to derive sufficient conditions for robust local ISS and IOS of the closed-loop system that is produced by the application of feedback linearising control to a nonlinear feedback linearisable system with unmodelled dynamics. Moreover, sufficient conditions for robust small-signal L-2-stability are derived by employing both the aforementioned nonlinear small-gain theorem and the well known small-gain theorem for L-2-stability. The conditions proposed are easily verifiable. A nontrivial illustrative example is included.