Exponential stabilisability of finite-dimensional linear systems with limited data rates. (English) Zbl 1012.93050

The authors consider the problem of exponentially stabilising a noiseless, finite-dimensional, linear time-invariant system under a feedback data rate constraint. Loosely speaking, the problem is converted into a moment stabilization, and in this framework, it is equivalent to finding a recursive quantiser for the initial state which yields exponentially diminishing error moments. Assuming that the initial state is random, the objective is to determine the least data rate above which there exists a coding and control law which makes the \(r\)th absolute state moment converge to zero faster than a specified exponential decay. The main theorem is stated, and the remainder of the paper gives details of the proof.


93D15 Stabilization of systems by feedback
90B18 Communication networks in operations research
93E15 Stochastic stability in control theory
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