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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

State observability and observer designs are investigated for linear-time-invariant systems in continuous time when the outputs are measured only at a set of irregular sampling time sequences. The problem is primarily motivated by systems with limited sensor information in which sensor switching generates irregular sampling sequences. State observability may be lost and the traditional observers may fail in general, even if the system has a full-rank observability matrix. It demonstrates that if the original system is observable, the irregularly sampled system will be observable if the sampling density is higher than some critical frequency, independent of the actual time sequences. This result extends Shannon's sampling theorem for signal reconstruction under periodic sampling to system observability under arbitrary sampling sequences. State observers and recursive algorithms are developed whose convergence properties are derived under potentially dependent measurement noises. Persistent excitation conditions are validated by designing sampling time sequences. By generating suitable switching time sequences, the designed state observers are shown to be convergent in mean square, with probability one, and with exponential convergence rates. Schemes for generating desired sampling sequences are summarized. [ABSTRACT FROM AUTHOR]