Stochastic Networked Control Systems with Dynamic Protocols

We consider networked control systems in which sensors, controllers, and actuators communicate through a shared network that introduces stochastic intervals between transmissions, delays and packet drops. Access to the communication medium is mediated by a protocol that determines which node (one of the sensors, one of the actuators, or the controller) is allowed to transmit a message at each sampling/actuator-update time. We provide conditions for mean exponential stability of the networked closed loop in terms of matrix inequalities, both for investigating the stability of given protocols, such as static round-robin protocols and dynamic maximum error first-try once discard protocols, and to design new dynamic protocols. The main result entailed by these conditions is that if the networked closed loop is stable for a static protocol then we can provide a dynamic protocol for which the networked closed loop is also stable. The stability conditions also allow for obtaining an observer-protocol pair that reconstructs the state of an LTI plant in a mean exponential sense and less conservative stability results than other conditions that previously appeared in the literature.