Network-Aware Design of State-Feedback Controllers for Linear Wireless Networked Control Systems

We study the problem of stabilizing the origin of a plant, modeled as a discrete-time linear system, for which the communication with the controller is ensured by a wireless network. The transmissions over the wireless channel are characterized by the so-called stochastic allowable transmission intervals (SATI), that is a stochastic version of the maximum allowable transmission interval (MATI). Instead of deterministic transmissions, SATI gives stability conditions in terms of the cumulative probability of successful transmission over N steps. We argue that SATI is well-suited for wireless networked control systems to cope both with the stochastic nature of the communications and the design of energy-efficient communication strategies. Our objective is to synthesize a stabilizing state-feedback controller and SATI parameters simultaneously. We model the overall closed-loop system as a Markov jump linear system and we first provide linear conditions for the stability of the wireless networked control systems in a mean-square sense. We then provide linear matrix inequalities conditions for the design of state-feedback controllers to ensure stability of the closed-loop system. These conditions can be used to obtain both the controller and the SATI. A numerical example is presented to illustrate our results.