Period-aware asymptotic gain with application to a periodically forced synchronization circuit
This work addresses a specific limitation in control theory for systems with periodic signals, offering incremental improvements in estimation accuracy.
The paper tackles the problem of estimating output bounds for systems with periodic inputs by introducing a period-aware asymptotic gain (PAG), which provides sharper asymptotic estimates than classical methods, as demonstrated through a numerical example in power electronics.
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.