Stabilization of Cascaded Two-Port Networked Systems with Simultaneous Nonlinear Uncertainties

TL;DR

This paper presents a comprehensive framework for analyzing the stability of networked control systems with nonlinear uncertainties in communication channels, providing a precise stability condition based on geometric insights and operator norms.

Contribution

It introduces a novel modeling approach for NCSs with cascaded nonlinear two-port networks and derives a necessary and sufficient stability condition involving arcsine bounds on uncertainties.

Findings

Provides a stability condition using arcsine of uncertainty bounds.

Models communication channels with distortion, interference, and nonlinearity.

Handles simultaneous uncertainties in plant, controller, and channels.

Abstract

We introduce a versatile framework to model and study networked control systems (NCSs). An NCS is described as a feedback interconnection of a plant and a controller communicating through a bidirectional channel modelled by cascaded nonlinear two-port networks. This model is sufficiently rich to capture various properties of a real-world communication channel, such as distortion, interference, and nonlinearity. Uncertainties in the plant, controller and communication channels can be handled simultaneously in the framework. We provide a necessary and sufficient condition for the robust finite-gain stability of an NCS when the model uncertainties in the plant and controller are measured by the gap metric and those in the nonlinear communication channels are measured by operator norms of the uncertain elements. This condition is given by an inequality involving "arcsine" of the uncertainty bounds and is derived from novel geometric insights underlying the robustness of a standard closed-loop system in the presence of conelike nonlinear perturbations on the system graphs.