Stability analysis of stochastic networked control systems

• Published in: Automatica (Oxford) Vol. 48; no. 5; pp. 917 - 925
• Main Authors: Donkers, M.C.F., Heemels, W.P.M.H., Bernardini, D., Bemporad, A., Shneer, V.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.05.2012; Elsevier
• Subjects: Applied sciences; Communication protocols; Computer science; control theory; systems; Computer systems and distributed systems. User interface; Control system analysis; Control systems; Control theory. Systems; Delay; Exact sciences and technology; Focusing; Intervals; Networked control systems; Parameter-varying systems; Preserves; Random variables; Software; Stability; Stochastic control; Stochasticity; Switched systems; System theory; Switched systems; Stochastic control; Communication protocols; Networked control systems; Parameter-varying systems; Linear control; Modeling; Hybrid system; Time varying system; Chemical reactor; Network analysis; Linear matrix inequality; Time interval; Random variable; Multimodel control; Packet switching; Statistical analysis; Probabilistic approach; Transmission protocol; Stochastic stability; Delay system; Distributed system; Transmission time; Random sequence; Stochastic analysis; Discrete time; Distributed control
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2012.02.029

In this paper, we study the stability of Networked Control Systems (NCSs) that are subject to time-varying transmission intervals, time-varying transmission delays, packet dropouts and communication constraints. The transmission intervals and transmission delays are described by a sequence of continuous random variables. The complexity that the continuous character of these random variables introduces is overcome using a novel convex overapproximation technique that preserves the available probabilistic information. By focusing on linear plants and controllers, we present a modelling framework for NCSs based on discrete-time linear switched and parameter-varying systems. Stability (in the mean-square) of these systems is analysed using a new stochastic computational technique, resulting in a finite number of linear matrix inequalities. We illustrate the developed theory on the benchmark example of a batch reactor.