Infimum Data Rates for Stabilising Markov Jump Linear Systems

Abstract

In recent years, the problem of stabilising linear dynamical systems with low feedback data rates has been intensively investigated. A particular focus has been the characterisation of the infimum data rate for stabilisability, which specifies the smallest rate, in bits per unit time, at which information can circulate in a stable feedback loop. This paper extends this line of research to the case of fully-observed, finite-dimensional, linear systems without process noise but with control-independent, Markov parameters. Unlike previous formulations, the coding alphabet is permitted to be random and time-varying via a possible dependence on the observed Markov modes. Using quantisation techni..