Stability robustness of feedback linearisable systems with input unmodelled dynamics

The stability robustness of a feedback linearisable system subject to unstr uctured 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 intercon nected systems that are characterised by both local ISS and IOS is establis hed. 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 o f 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 nonli near small-gain theorem and the well known small-gain theorem for L-2-stabi lity. The conditions proposed are easily verifiable. A nontrivial illustrat ive example is included.