Internal stability of dynamic quantised control for stochastic linear plants

Abstract

Existing analyses of 'zooming' quantisation schemes for bit-rate-limited control systems rely on the encoder and controller being initialised with identical internal states. Due to the quantiser discontinuity and the plant instability, it was not clear if closed-loop stability was possible if the encoder and controller commenced from different initial conditions. In this article, we consider partially observed, unstable linear time-invariant plants, with unbounded and possibly non-Gaussian noise, and propose a modified zooming-like scheme with finite-dimensional internal encoder and controller states that may not initially be identical. Using a stochastic pseudo-norm, we prove that this sche..