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

摘要

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> 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 <emphasis emphasistype="boldital">Proceedings of the 44th IEEE Conference on Decision and Control</emphasis>. 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 <formula formulatype="inline"><tex>$L_p$</tex></formula> stability from exogenous disturbance to NCS state with a linear finite expected gain. Within the same framework, we extend the results of NeŠiĆ and Teel (see <emphasis emphasistype="boldital">IEEE Trans. Autom. Control</emphasis>, 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. </para>