  Self-triggered control (STC) is a resource efficient approach to determine
sampling instants for Networked Control Systems. At each sampling instant, an
STC mechanism determines not only the control inputs but also the next sampling
instant. In this article, an STC framework for perturbed nonlinear systems is
proposed. In the framework, a dynamic variable is used in addition to current
state information to determine the next sampling instant, rendering the STC
mechanism dynamic. Using dynamic variables has proven to be powerful for
increasing sampling intervals for the closely related concept of
event-triggered control, but has so far not been exploited for STC. Two
variants of the dynamic STC framework are presented. The first variant can be
used without further knowledge on the disturbance and leads to guarantees on
input-to-state stability. The second variant exploits a known disturbance bound
to determine sampling instants and guarantees asymptotic stability of a set
containing the origin. In both cases, hybrid Lyapunov function techniques are
used to derive the respective stability guarantees. Different choices for the
dynamics of the dynamic variable, that lead to different particular STC
mechanisms, are presented for both variants of the framework. The resulting
dynamic STC mechanisms are illustrated with two numerical examples to emphasize
their benefits in comparison to existing static STC approaches.

Systems and Control;Systems and Control