Stabilization of Cascaded Two-Port Networked Systems Against Nonlinear Perturbations

TL;DR

This paper analyzes the robust stability of cascaded two-port networked control systems under nonlinear perturbations, providing necessary and sufficient conditions based on geometric insights and uncertainty bounds.

Contribution

It introduces a stability criterion for two-port NCS with nonlinear uncertainties, using geometric analysis to derive a necessary and sufficient stability condition.

Findings

Robust stability is guaranteed when nonlinear uncertainties are small.

Stability condition expressed via arcsin of uncertainty bounds.

The stability criterion is both necessary and sufficient.

Abstract

A networked control system (NCS) consisting of cascaded two-port communication channels between the plant and controller is modeled and analyzed. Towards this end, the robust stability of a standard closed-loop system in the presence of conelike perturbations on the system graphs is investigated. The underlying geometric insights are then exploited to analyze the two-port NCS. It is shown that the robust stability of the two-port NCS can be guaranteed when the nonlinear uncertainties in the transmission matrices are sufficiently small in norm. The stability condition, given in the form of "arcsin" of the uncertainty bounds, is both necessary and sufficient.