On Feedback Capability in a Class of Nonlinearly Parameterized Uncertain Systems

In this technical note, we will investigate the maximum capability and limitations of the feedback mechanism in globally stabilizing a basic class of discrete-time nonlinearly parameterized dynamical systems with multiple unknown parameters. Both "possibility" and "impossibility" theorems together with a fairly complete characterization on the capability of feedback will be presented. It will be seen that to characterize the feedback capability, the growth rates of the sensitivity functions of the nonlinear dynamics with respect to the uncertain parameters play a crucial role, and a suitable decomposition of the family of the nonlinearly parameterized functions in question turns out to be necessary.