Internal stability of dynamically quantised control for stochastic scalar plants

Abstract

In this paper we study conditions under which an unstable stochastic scalar linear plant with unbounded noise can be internally stabilised using 'zooming'-like coding and control schemes having dynamic, finitedimensional internal states. Such structures are known to be needed in communicationconstrained control when no bound on the plant noise is available. However, previous schemes were based on coders and controllers starting with identical internal states. In this paper, we remove this assumption and explicitly construct a finite-dimensional coding and control policy that yields mean square stability of all state variables, for a random initial plant state and arbitrary initial encoder an..