  This paper proposes a new methodology in linear time-periodic (LTP) system
identification. In contrast to previous methods that totally separate dynamics
at different tag times for identification, the method focuses on imposing
appropriate structural constraints on the linear time-invariant (LTI)
reformulation of LTP systems. This method adopts a periodically-switched
truncated infinite impulse response model for LTP systems, where the structural
constraints are interpreted as the requirement to place the poles of the
non-truncated models at the same locations for all sub-models. This constraint
is imposed by combining the atomic norm regularization framework for LTI
systems with the group lasso technique in regression. As a result, the
estimated system is both uniform and low-order, which is hard to achieve with
other existing estimators. Monte Carlo simulation shows that the grouped atomic
norm method does not only show better results compared to other regularized
methods, but also outperforms the subspace identification method under high
noise levels in terms of model fitting.
