Robust stability under asynchronous sensing and control

We address the stability of networked control systems in which a sensor and an output-feedback controller operate asynchronously, which leads to uncertainty in the sampling instants. In addition, we also consider polytopic uncertainty in the plant model. The analysis is based on transforming the closed-loop system into an impulsive system, by considering an extended state variable that includes the states of the continuous-time plant and the discrete-time controller. We provide a sufficient condition for the robust stability of the closed-loop system in terms of linear matrix inequalities. This condition is based on the construction of a continuous-time Lyapunov functional that also incorporates the discrete-time state of the digital controller. We illustrate the obtained result with numerical simulations.