Finite-sample-based Spectral Radius Estimation and Stabilizability Test for Networked Control Systems

TL;DR

This paper introduces finite-sample methods to estimate the spectral radius of system matrices and test stabilizability in networked control systems with lossy channels, using limited data and probabilistic error bounds.

Contribution

It proposes novel finite-sample spectral radius estimation techniques and stabilizability tests applicable to networked control systems with data constraints.

Findings

Two spectral radius estimation methods with high-probability error bounds

A stabilizability test for NCSs using finite data samples

Validation of methods through theoretical analysis and simulations

Abstract

In the analysis and control of discrete-time linear time-invariant systems, the spectral radius of the system state matrix plays an essential role. Usually, it is assumed that system matrices are known, from which the spectral radius can be directly computed. Instead, we consider the setting where the system is affected by process noise, and one has only finitely many samples of system input and state measurements. We provide two methods for estimating the spectral radius and derive error bounds that hold with high probability. Moreover, we show how to use the derived results to test stabilizability for networked control systems (NCSs) with lossy channels when only finitely many samples of the system input, state, and packet drop sequence are available.