Robustness of Large-Gain Linearizing Feedback in the Presence of Fast Dynamics

One major advantage of feedback linearization design is to trasform a nonlinear system (or part of a nonlinear system) into a specific linear canonical form such that the closed-loop system can have excellent performance with arbitrarily large gains and global stability. In this paper, we show that if fast parasite modes exist such that the dimension of the nominal model is smaller than the actual system, the closed-loop system destabilizes at large gain if a certain stability condition is violated. Moreover, global stability can be lost even before the critical gain value is exceeded and the domain of attraction of the origin decreases with increasing gain. This lack of robustness to high-frequency disturbances occurs even when the nonlinearities and parameters of the nominal system are known exactly. Since chemical systems are plagued with unknown fast dynamics, the applicability of feedback linearization designs is hence severely restricted.