Stabilizing transmission intervals for Networked Control Systems with nonlinear delay dynamics

In this paper, we consider a nonlinear delay process to be controlled over a communication network in the presence of disturbances and study robustness of the resulting closed-loop system with respect to network-induced phenomena such as sampled, distorted and delayed data as well as scheduling protocols. In particular, we compute the Maximally Allowable Transfer Interval (MATI) for which a prescribed ℒ
p
-gain, as a measure of control performance, is attained. The proposed methodology combines impulsive delay system modeling with Lyapunov-Razumikhin techniques to allow for communication delays greater than MATIs. Other salient features of our methodology are the consideration of nonuniform variable delays and employment of model-based estimators to prolong MATIs. The present stability results are provided for the class of Uniformly Globally Exponentially Stable (UGES) scheduling protocols such as Round Robin (RR) and Try-Once-Discard (TOD). Finally, a nonlinear example is provided to demonstrate the benefits of our methodology.