Stabilization over Gaussian Finite‐State Markov Channels

Abstract

Chapter 3 studies the mean-square stabilization problem of discrete-time linear time-invariant systems over Gaussian finite-state Markov channels, which suffer from both signal-to-noise ratio constraint and correlated channel fading modeled by a Markov process. The existence of a fundamental limitation for mean-square stabilization is first established. Then, sufficient stabilization conditions under a time division multiple access (TDMA) communication scheme are derived in terms of the stability of a Markov jump linear system. Moreover, we present a necessary and sufficient condition for mean-square stabilization of two-dimensional systems controlled over power-constrained Markov lossy channels. Furthermore, improved sufficient stabilization conditions are derived based on an adaptive TDMA communication scheme for general high-dimensional systems, which achieve a larger stabilization region than the TDMA communication scheme.