Input-Output Stability of Networked Control Systems With Stochastic Protocols and Channels

• Published in: IEEE transactions on automatic control Vol. 53; no. 5; pp. 1160 - 1175
• Main Authors: Tabbara, M., Nesic, D.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.06.2008; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Access protocols; Applied sciences; Computer science; control theory; systems; Computer systems and distributed systems. User interface; Control systems; Control theory. Systems; Ethernet networks; Exact sciences and technology; Gain; Multiaccess communication; Networked control systems; Networked control systems (NCS); Process control. Computer integrated manufacturing; protocols; Software; Stability; Stochastic processes; Stochastic systems; Studies; Wireless application protocol; Multiple access; Packet switching; Input-output stability; Probabilistic approach; Networked control systems (NCS); Collision; Transmission protocol; Lyapunov method; Distributed system; Stochastic system; Transmission time; Uncertain system; Analog; Ethernet; Distributed control; Network protocol; stochastic systems; Stochastic control; Wireless network; Access protocol; protocols; Deterministic approach; Lyapunov function
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2008.923691

This paper introduces a new definition of stochastic protocols for networked control systems (NCS) and the stochastic analog of the notion of uniform persistency of excitation of protocols first presented in the Proceedings of the 44th IEEE Conference on Decision and Control. Our framework applies directly to common wireless and wireline NCS, including those built on carrier-sense multiple access (CSMA) style protocols, with Ethernet and 802.11a/b/g as prime examples of this class. We present conditions for a general class of nonlinear NCS with exogenous disturbances using stochastic protocols in the presence of packet dropouts, random packet transmission times and collisions that are sufficient for L P stability from exogenous disturbance to NCS state with a linear finite expected gain. Within the same framework, we extend the results of Nesic and Teel (see IEEE Trans. Autom. Control, vol. 49, no. 10, pp. 1650-1667, Oct. 2004) to provide an analysis of deterministic protocols, including try-once-discard (TOD), in the presence of random packet dropouts and intertransmission times and provide a stochastic analog of the Lyapunov-theoretic stability properties for network protocols introduced therein.