Stability Analysis of Networked Control Systems Using a Switched Linear Systems Approach

Abstract

In this paper, we study the stability of Networked Control Systems (NCSs) that are subject to time-varying transmission intervals and communication constraints in the sense that, per transmission, only one node can access the network and send its information. The order in which nodes send their information is dictated by a network protocol, such as the well-known Round Robin (RR) or Try-Once-Discard (TOD) protocol. Focussing on linear plants and linear continuous-time or discrete-time controllers, we model the NCS with time-varying transmission intervals as a discrete-time switched linear uncertain system. We obtain bounds for the allowable range of transmission intervals in terms of both minimal and maximal allowable transmission intervals. Hereto, a new convex overapproximation of the uncertain switched system is proposed, using a polytopic system with norm-bounded uncertainty, and new stability results for this class of hybrid systems are developed. On the benchmark example of a batch reactor, we explicitly exploit the linearity of the system, leading to a significant reduction in conservatism with respect to the existing approaches.