# Stabilizability of Markov jump linear systems modeling wireless networked control scenarios (extended version)

## TL;DR

This paper establishes necessary and sufficient conditions for the stabilizability of wireless networked control systems modeled as Markov jump linear systems with packet losses, crucial for ensuring system stability under realistic wireless channel conditions.

## Contribution

It derives the fundamental stabilizability conditions for Markov jump linear systems with delayed mode observations, extending prior work on optimal control to stability analysis.

## Key findings

- Derived necessary and sufficient stabilizability conditions.
- Illustrated conditions with a WirelessHART-based example.
- Showed importance of these conditions for systems with Bernoulli packet loss models.

## Abstract

The communication channels used to convey information between the components of wireless networked control systems (WNCSs) are subject to packet losses due to time-varying fading and interference. The WNCSs with missing packets can be modeled as Markov jump linear systems with one time-step delayed mode observations. While the problem of the optimal linear quadratic regulation for such systems has been already solved, we derive the necessary and sufficient conditions for stabilizability. We also show, with an example considering a communication channel model based on WirelessHART (a on-the-market wireless communication standard specifically designed for process automation), that such conditions are essential to the analysis of WNCSs where packet losses are modeled with Bernoulli random variables representing the expected value of the real random process governing the channel.