Exponential stabilisability of finite-dimensional linear systems with limited data rates

A critical notion in the field of communication-limited control is the smallest data rate above which there exists a stabilising coding and control law for a given plant. This quantity measures the lowest rate at which information can circulate in a stable feedback loop and provides a practical guideline for the allocation of communication resources. In this paper, the exponential stabilisability of finite-dimensional LTI plants with limited feedback data rates is investigated. By placing a probability density on the initial state and casting the objective in terms of state moments, the problem is shown to be similar to one in asymptotic quantisation. Quantisation theory is then applied to obtain the infimum stabilising data rate over all causal coding and control laws, under mild requirements on the initial state density. (C) 2003 Elsevier Science Ltd. All rights reserved.