On Stabilizability of Nonlinearly Parameterized Discrete-Time Systems

Most existing works on adaptive control of discrete-time systems focus on the case of linear parametrization. For nonlinearly parameterized systems, the stabilizability turns out to be an intractable issue. This technical note is devoted to seeking the essential factors that determine the stabilizability of nonlinearly parameterized discrete-time systems. A sufficient condition imposed on the structures of the system functions is established. Analysis shows that the sensitivity function of unknown parameters plays a crucial role in characterizing the uncertainties of parameterized systems. One of the implications of this result is that arbitrarily growing nonlinearities in the uncertain model may be allowed for global stabilization.