Controllability of a Class of Nonlinear Networked Systems

TL;DR

This paper investigates the controllability of nonlinear, heterogeneous networked systems by analyzing a linear system with nonlinear perturbations under Holder and Lipschitz conditions, employing fixed point theorems.

Contribution

It extends controllability analysis to nonlinear perturbed networked systems using fixed point theory, which is less explored in existing literature.

Findings

Controllability is established for nonlinear perturbed systems under specific conditions.

Theoretical results are supported by numerical examples.

The approach applies fixed point theorems to nonlinear networked systems.

Abstract

Various controllability conditions have been obtained by researchers for heterogeneous networked systems with linear dynamics. However, the literature for nonlinear, heterogeneous networked systems is comparatively less. In this paper we analyse the controllabiity aspect of a nonlinearly perturbed linear networked system. The basic assumption is that the linear system is controllable and the nonlinear perturbation functions satisfy Holder continuity condition and in particular Lipschitz condition. The Boyd-Wong fixed point theorem is employed to prove controllability of the nonlinear system. The result is illustrated with numerical examples.