Mp. Tzamtzi et Sg. Tzafestas, Stability robustness of feedback linearisable systems with input unmodelled dynamics, IEE P-CONTR, 146(1), 1999, pp. 77-83
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.