Finite data-rate stabilization of a switched linear system with unknown disturbance*

Abstract: We study the stabilization of a switched linear system with unknown disturbance using sampled and quantized state feedback. The switching is slow in the sense of combined dwell-time and average dwell-time, while the active mode is unknown except at sampling times. Each mode of the switched system is stabilizable, and the disturbance admits an unknown bound. A communication and control strategy is designed to achieve practical stability and exponential convergence w.r.t. the initial state with a nonlinear gain on the disturbance, provided the data-rate meets given lower bounds. Compared with previous results, a more involved algorithm is developed to handle effects of the unknown disturbance based on employing an iteratively updated estimate of the disturbance bound and expanding the over-approximations of reachable sets over sampling intervals from the case without disturbance.