Mean Square Stabilization of Vector LTI Systems over Power Constrained Lossy Channels

TL;DR

This paper addresses the challenge of stabilizing vector linear time-invariant systems over power-constrained lossy communication channels by designing adaptive scheduling strategies that improve stabilization conditions.

Contribution

It introduces an adaptive TDMA scheduler that outperforms conventional methods and provides optimal solutions for two-dimensional systems, establishing necessary and sufficient stabilization conditions.

Findings

Adaptive TDMA scheduler achieves larger stabilizability region.

Optimal scheduler for two-dimensional systems established.

Necessary and sufficient conditions for stabilization derived.

Abstract

This paper studies the mean square stabilization problem of vector LTI systems over power constrained lossy channels. The communication channel is with packet dropouts, additive noises and input power constraints. To overcome the difficulty of optimally allocating channel resources among different sub-dynamics, schedulers are designed with time division multiplexing of channels. An adaptive TDMA (Time Division Multiple Access) scheduler is proposed first, which is shown to be able to achieve a larger stabilizability region than the conventional TDMA scheduler, and is optimal under some special cases. In particular, for two-dimensional systems, an optimal scheduler is designed, which provides the necessary and sufficient condition for mean square stabilization.