Speaker
Description
We consider single-input, single-output systems with time-varying, periodic parameters:
ẋ(t) = A(t)x(t) + b(t)u(t),
y(t) = c(t) x(t),
where A(t) ∈ ℝⁿˣⁿ and b(t), c(t) ∈ ℝⁿ all have period T.
Such systems arise when modeling phenomena in fluid dynamics, structural mechanics, and electronic circuits. In particular, linearization around known periodic orbits of a nonlinear model produces a periodic system of partial differential equations, and subsequent spatial semi-discretization yields large-scale linear time-periodic (LTP) dynamical systems. The need to simulate system responses to a variety of inputs motivates the development of effective model reduction tools for these systems.
While research on model reduction for LTP systems is relatively limited, there is a substantial body of literature devoted to control, spectral analysis, and harmonic response of LTP systems. From this literature arise the Harmonic Transfer Function and the H₂ norm for LTP systems. These concepts lead to necessary conditions for an H₂-optimal reduced-order model. In the linear time-invariant case, the Iterative Rational Krylov Algorithm (IRKA) is a standard approach for the H₂ model reduction problem. The work presented here extends IRKA to the LTP setting.