On Floquet-Fourier Realizations of Linear Time-Periodic Impulse Responses

We show that a linear time-periodic system with a smooth impulse response can be arbitrarily well approximated by a linear time-periodic state-space representation in so-called Floquet-Fourier form. The Floquet-Fourier form has a constant state matrix and the input and output matrices have only finitely many nonzero Fourier coefficients. Such representations are easier to use for analysis and control design than the impulse response or fully general state-space forms. The construction of the Floquet-Fourier form is done using methods for model approximation of infinite-dimensional linear time-invariant systems. We also propose a method for constructing minimal realizations from impulse responses of a special structure