Network-based control via a novel analysis of hybrid systems with time-varying delays

This paper studies the stabilization of Networked Control Systems (NCS) with communication constraints, variable delays and variable sampling intervals. The system sensor nodes are supposed to be distributed over a network. The scheduling of sensor information towards the controller is ruled by a quadratic protocol. This protocol first compares the weighted errors of the signals in individual nodes, where the error is the difference between the most recently activated signal at the sensor side and its current value, and then transmits the measurement from the node with the largest error. The closed-loop system has the form of a hybrid system with delays in the continuous dynamics and in the reset conditions. A new Lyapunov-Krasovskii method is developed for the partial exponential stability with respect to the x-variable of the delayed hybrid system. Polytopic uncertainties in the system model can be easily included in our analysis. The efficiency of the time-delay approach is illustrated on the cart-pendulum and the batch reactor benchmark problems. Our results improve the hybrid system-based ones and allow non-small network-induced delay.