  This note studies (practical) asymptotic stability of nonlinear networked
control systems whose protocols are not necessarily uniformly globally
exponentially stable. In particular, we propose a Lyapunov-based approach to
establish (practical) asymptotic stability of the networked control systems.
Considering so-called modified Round Robin and Try-Once-Discard protocols,
which are only uniformly globally asymptotically stable, we explicitly
construct Lyapunov functions for these two protocols, which fit our proposed
setting. In order to optimize the usage of communication resource, we exploit
the following transmission policy: wait for a certain minimum amount of time
after the last sampling instant and then check a state-dependent criterion.
When the latter condition is violated, a transmission occurs. In that way, the
existence of the minimum amount of time between two consecutive transmission is
established and so-called Zeno phenomenon, therefore, is avoided. Finally,
illustrative examples are given to verify the effectiveness of our results.
