Abstract
In this paper, we present a quantization scheme that reconstructs the state of switched linear systems with a prescribed exponential decaying rate for the state estimation error. We show how to use the Lyapunov exponents and a geometric object called Oseledets' filtration to design such a quantization scheme. Then, we prove that this algorithm works at an average data-rate close to the estimation entropy of the given system. Furthermore, we can choose the average data-rate to be arbitrarily close to the estimation entropy whenever the switched linear system has the so-called regularity property. We show that, under the regularity assumption, the quantization scheme is completely causal in the sense that it only depends on information that is available at the current time instant. Finally, we present simulation results for a Markov Jump Linear System, a class of systems for which the realizations are known to be regular with probability 1.
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