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

This paper introduces a new definition of stochastic protocols for networked control systems (NCS) and the stochastic analogue of the notion of uniform persistency of excitation of protocols first presented in [1]. Our framework applies directly to common wireless and wireline NCS, including those built on collision-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 Lp stability from exogenous disturbance to NCS state with a linear finite expected gain. Within the same framework, we extend the results of [2] to provide an analysis of deterministic protocols, including try-oncediscard (TOD), in the presence of random packet dropouts and inter-transmission times and provide a stochastic analogue of the Lyapunov-theoretic stability properties for network protocols introduced therein.