  In this paper, we propose a novel sampling control framework based on the
emulation technique where the sampling error is regarded as an auxiliary input
to the emulated system. Utilizing the supremum norm of sampling error, the
design of periodic sampling and event-triggered control law renders the error
dynamics bounded-input-bounded-state (BIBS), and when coupled with system
dynamics, achieves global or semi-global stabilization. The proposed framework
is then extended to tackle the event-triggered and periodic sampling
stabilization for a system where only partial state is available for feedback
and the system is subject to parameter uncertainties. The proposed framework is
further extended to solve two classes of event-triggered adaptive control
problems where the emulated closed-loop system does not admit an input-to-state
stability (ISS) Lyapunov function. For the first class of systems with linear
parameterized uncertainties, even-triggered global adaptive stabilization is
achieved without the global Lipschitz condition on nonlinearities as often
required in the literature. For the second class of systems with uncertainties
whose bound is unknown, the event-triggered adaptive (dynamic) gain controller
is designed for the first time. Finally, theoretical results are verified by
two numerical examples.
