Existence and continuity of solution trajectories of generalized equations with application in electronics

TL;DR

This paper investigates how perturbations in input signals affect the solution trajectories of generalized equations in electronic circuits, establishing conditions for their existence and continuity using variational analysis and metric regularity.

Contribution

It introduces a novel application of strong metric regularity to analyze the stability and continuity of solution trajectories in parametric generalized equations for electronic circuits.

Findings

Proves regularity properties of solution trajectories under perturbations

Establishes the existence of continuous solution trajectories

Uses uniform strong metric regularity to ensure trajectory stability

Abstract

We consider a special form of parametric generalized equations arising from electronic circuits with AC sources and study the effect of perturbing the input signal on solution trajectories. Using methods of variational analysis and strong metric regularity property of an auxiliary map, we are able to prove the regularity properties of the solution trajectories inherited by the input signal. Furthermore, we establish the existence of continuous solution trajectories for the perturbed problem. This can be achieved via a result of uniform strong metric regularity for the auxiliary map. Key words and phrases: generalized equations, electronic circuits, strong metric regularity, uniform strong metric regularity, perturbations.