Networked control systems in the presence of scheduling protocols and communication delays

TL;DR

This paper presents a novel hybrid system model and Lyapunov-Krasovskii method for analyzing the stability of networked control systems with variable delays, scheduling protocols, and communication constraints, including delays exceeding sampling intervals.

Contribution

It introduces a new hybrid system model with time-varying delays and a Lyapunov-Krasovskii approach for stability analysis, accommodating delays greater than sampling intervals.

Findings

Effective stability analysis for NCS with large delays.

Application to uncertain cart-pendulum and batch reactor examples.

Inclusion of polytopic uncertainties in the model.

Abstract

This paper develops the time-delay approach to Networked Control Systems (NCSs) in the presence of variable transmission delays, sampling intervals and communication constraints. The system sensor nodes are supposed to be distributed over a network. Due to communication constraints only one node output is transmitted through the communication channel at once. The scheduling of sensor information towards the controller is ruled by a weighted Try-Once-Discard (TOD) or by Round-Robin (RR) protocols. Differently from the existing results on NCSs in the presence of scheduling protocols (in the frameworks of hybrid and discrete-time systems), we allow the communication delays to be greater than the sampling intervals. A novel hybrid system model for the closed-loop system is presented that contains {\it time-varying delays in the continuous dynamics and in the reset conditions}. A new Lyapunov-Krasovskii method, which is based on discontinuous in time Lyapunov functionals is introduced for the stability analysis of the delayed hybrid systems. Polytopic type uncertainties in the system model can be easily included in the analysis. The efficiency of the time-delay approach is illustrated on the examples of uncertain cart-pendulum and of batch reactor.