Period-aware asymptotic gain with application to a periodically forced synchronization circuit

TL;DR

This paper introduces the period-aware asymptotic gain (PAG), a new concept that leverages input periodicity to provide sharper output bounds and analyze frequency-dependent behaviors in periodically forced systems.

Contribution

The paper proposes PAG, a novel gain measure that improves asymptotic output estimation for periodic inputs, enabling analysis of bandwidth and resonance effects.

Findings

PAG can distinguish between high-frequency and low-frequency signals.

PAG provides tighter bounds than classical AG for periodic inputs.

Numerical example demonstrates PAG's application in power electronics.

Abstract

The classical asymptotic gain (AG) is a concept known from the input-to-state stability theory. Given a uniform input bound, AG estimates the asymptotic bound of the output. Sometimes, however, more information is known about the input than just a bound. In this paper we consider the case of a periodic input. Under the assumption that the system converges to a periodic solution, we introduce a new gain, called period-aware asymptotic gain (PAG), which employs periodicity to enable a sharper asymptotic estimation of the output. Since the PAG can distinguish between short-period ("high-frequency") and long-period ("low-frequency") signals, it is able to rigorously quantify such properties as bandwidth, resonant behavior, and high-frequency damping. We discuss how the PAG can be computed and illustrate it with a numerical example from the field of power electronics.