H2 and H∞ norm computations of linear continuous-time periodic systems via the skew analysis of frequency response operators

Abstract

The H 2 and H ∞ norm computations of finite-dimensional linear continuous-time periodic (FDLCP) systems through the frequency response operators defined by steady-state analysis are discussed. By the skew truncation, the H 2 norm can be reached to any degree of accuracy by that of an asymptotically equivalent linear time-invariant (LTI) continuous-time system. The H ∞ norm can be approximated by the maximum singular value of the frequency response of an asymptotically equivalent LTI continuous-time system over a certain frequency range via the modified skew truncation. By the latter result, a Hamiltonian test is proved for FDLCP systems in an LTI fashion, based on which a modified bisection algorithm is developed.