Title: Linear time-periodic dynamical systems: An H2 analysis and a model reduction framework,
Abstract: Linear time-periodic (LTP) dynamical systems frequently appear in the
modeling of phenomena related to fluid dynamics, electronic circuits, and
structural mechanics via linearization centered around known periodic orbits of
nonlinear models. Such LTP systems can reach orders that make repeated
simulation or other necessary analysis prohibitive, motivating the need for
model reduction.
We develop here an algorithmic framework for constructing reduced models that
retains the linear time-periodic structure of the original LTP system. Our
approach generalizes optimal approaches that have been established previously
for linear time-invariant (LTI) model reduction problems. We employ an
extension of the usual H2 Hardy space defined for the LTI setting to
time-periodic systems and within this broader framework develop an a posteriori
error bound expressible in terms of related LTI systems. Optimization of this
bound motivates our algorithm. We illustrate the success of our method on two
numerical examples.