FINITE-DIMENSIONAL MODELS IN EVALUATING THE H2 NORM OF CONTINUOUS-TIME PERIODIC SYSTEMS

Abstract

Finite-dimensional harmonic models for the H2 norm evaluation of finite-dimensional linear continuous-time periodic (FDLCP) systems are derived, which are expressed explicitly through finitely many Fourier coefficients of the system matrices, and thus dispense with the transition matrix knowledge of any FDLCP models, as opposed to most existing methods in the literature. This paper also shows that the skew- and square-truncated counterparts to the harmonic state operator are invertible in a class of stable FDLCP systems. This invertibility fact, together with the 2-regularized determinant technique about Hilbert-Schmidt operators, plays a key role in justifying the multiple-step truncation on the unbounded harmonic state operators of FDLCP systems and establishing rigorous convergence arguments for the proposed H2 norm formulae and the associated finite-dimensional harmonic models.