Stochastic maximum allowable transmission intervals for the stability of linear wireless networked control systems

We investigate the scenario where a plant, modeled as a linear deterministic discrete-time system, is controlled through a wireless communication network. The controller is designed by emulation, meaning that we construct it to stabilize the origin of the plant while ignoring communication constraints and then implement the control law over the network. The transmissions over the wireless channel are time-varying and uncertain, in particular, the probability of successful communication (i.e., no packet is dropped) between the plant and the controller depends on the resources utilized, such as the allocated bandwidth or the transmission signal power. As a result, we provide conditions on the varying inter-transmission times to ensure the mean square stability of the closed-loop system. The novelty is that stability properties are characterized by not only the length of the inter-transmission interval (often called the MATI in the deterministic literature) but also by the probability of successful communication before and after this interval, referred to as the stochastic allowable transmission interval (SATI). These conditions could then be utilized by radio engineers/researchers to design energy-efficient communication strategies while ensuring the mean square stability of the control system.