Stabilization of Linear Systems Across a Time-Varying AWGN Fading Channel

TL;DR

This paper determines the minimum average transmit power needed for stabilizing a linear system over a time-varying AWGN fading channel using optimal power adaptation, considering different fading models.

Contribution

It provides necessary and sufficient conditions for stabilization and formulates the power minimization as a geometric program, advancing control over fading channels.

Findings

Minimum power for stabilization can be computed via geometric programming.

Stabilization conditions depend on channel state information and fading characteristics.

Optimal power adaptation reduces transmit power while ensuring system stability.

Abstract

This technical note investigates the minimum average transmit power required for mean-square stabilization of a discrete-time linear process across a time-varying additive white Gaussian noise (AWGN) fading channel that is presented between the sensor and the controller. We assume channel state information at both the transmitter and the receiver, and allow the transmit power to vary with the channel state to obtain the minimum required average transmit power via optimal power adaptation. We consider both the case of independent and identically distributed fading and fading subject to a Markov chain. Based on the proposed necessary and sufficient conditions for mean-square stabilization, we show that the minimum average transmit power to ensure stabilizability can be obtained by solving a geometric program.