Feedback Stabilization of Switched Linear Systems With Unknown Disturbances Under Data-Rate Constraints

We study the problem of stabilizing a switched linear system with a completely unknown disturbance using sampled and quantized state feedback. The switching is assumed to be slow enough in the sense of combined dwell time and average dwell time, each individual mode is assumed to be stabilizable, and the data rate is assumed to be large enough but finite. By extending the approach of reachable-set approximation and propagation from an earlier result on the disturbance-free case, we develop a communication and control strategy that achieves a variant of input-to-state stability with exponential decay. An estimate of the disturbance bound is introduced to counteract the unknown disturbance, and a novel algorithm is designed to adjust the estimate and recover the state when it escapes the range of quantization.