The generalized Kalman-Yakubovich-Popov lemma as established by Iwasaki and
Hara in 2005 marks a milestone in the analysis and synthesis of linear systems
from a finite-frequency perspective. Given a pre-specified frequency band, it
allows us to produce passive controllers with excellent in-band disturbance
attenuation performance at the expense of some of the out-of-band performance.
This paper focuses on control design of linear systems in the presence of
disturbances with non-strictly or non-stationary limited frequency spectrum. We
first propose a class of frequency-dependent excited energy functions (FD-EEF)
as well as frequency-dependent excited power functions (FD-EPF), which possess
a desirable frequency-selectiveness property with regard to the in-band and
out-of-band excited energy as well as excited power of the system. Based upon a
group of frequency-selective passive controllers, we then develop a
frequency-dependent switching control (FDSC) scheme that selects the most
appropriate controller at runtime. We show that our FDSC scheme is capable to
approximate the solid in-band performance while maintaining acceptable
out-of-band performance with regard to global time horizons as well as
localized time horizons. The method is illustrated by a commonly used benchmark
model