Stability Conditions for Remote State Estimation of Multiple Systems over Semi-Markov Fading Channels

TL;DR

It is shown that, from a system stability perspective, fast fading channels may be preferable to slow fading ones and the model is sufficiently general to be used in both fast and slow fading scenarios.

Abstract

This work studies remote state estimation of multiple linear time-invariant systems over shared wireless time-varying communication channels. We model the channel states by a semi-Markov process which captures both the random holding period of each channel state and the state transitions. The model is sufficiently general to be used in both fast and slow fading scenarios. We derive necessary and sufficient stability conditions of the multi-sensor-multi-channel system in terms of the system parameters. We further investigate how the delay of the channel state information availability and the holding period of channel states affect the stability. In particular, we show that, from a system stability perspective, fast fading channels may be preferable to slow fading ones.

Figures (3)

• Figure 1: The multi-sensor-multi-frequency remote estimator. P, S, G, and RE denote processes, sensors, gateway and remote estimator, respectively.
• Figure 2: An illustration of the semi-Markov chain of $\{\mathbf{h}(t)\}$.
• Figure 3: Stability regions (gray colored) with $\tilde{d}_{21} = 0.2, \tilde{d}_{22} = 0.9$ in (a) and $\tilde{d}_{21} = 0.9, \tilde{d}_{22} = 0.9$ in (b), where the solid, doted, and dashed lines indicate the regions with $\tilde{\psi}_1=0.99, 0.5$, and $0.1$, respectively.

Theorems & Definitions (11)

• Definition 1: Average Mean-Square Stability
• Lemma 1
• Theorem 1
• Remark 1
• proof : Proof of Necessity
• Lemma 2
• Lemma 3
• proof : Proof of Sufficiency
• Remark 2
• Theorem 2