Stabilizing a switched linear system with disturbance by sampled-data quantized feedback

We study the problem of stabilizing a switched linear system with disturbance using sampled and quantized measurements of its state. The switching is assumed to be 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 linear system is assumed to be stabilizable, and the magnitude of the disturbance is constrained by a known bound. A communication and control strategy is designed to guarantee bounded-input-bounded-state (BIBS) stability of the switched linear system and an exponential convergence rate with respect to the initial state, providing the data rate satisfies certain lower bounds. Such lower bounds are established by expanding the over-approximation bounds of reachable sets over sampling intervals derived in a previous paper to accommodate effects of the disturbance.

I. Introduction

Feedback control problems with limited information have been an active research area for years, as surveyed by Nair et al. [1]. Information flow in a feedback loop has been an important factor in many application-related scenarios, not only because of bandwidth constraints, but for cost concerns, physical restrictions, and security considerations as well. Besides the aforementioned practical motivations, the question of how much information is required to achieve a certain control objective is quite fundamental and intriguing from the theoretical point of view. In the study of feedback control problems, it is common to characterize the limitation on information flow as a finite data transmission rate achieved by using sampled and quantized measurements to generate the control input (see, e.g., [2], [3] and [4], Ch. 5), which is the modeling framework adopted in this paper.