Implementing the Hamiltonian test for the H∞ norm in linear continuous-time periodic systems

By the Floquet similarity transformations of finite-dimensional linear continuous-time periodic (FDLCP) systems, the time-domain Hamiltonian test for the H∞ norm is first interpreted in terms of Toeplitz operators of the system matrices. Based on this novel frequency-domain interpretation, implementing the time-domain Hamiltonian test can be accomplished by working on its frequency-domain counterpart via truncations. This gives us a bisection algorithm for evaluating the H∞ norm of a class of FDLCP systems through finite-dimensional linear time-invariant continuous-time models. The finite-dimensional Hamiltonian test is necessary and sufficient in the asymptotic sense, and claimed only via Fourier coefficients of the system matrices without the transition matrix of the FDLCP system concerned. There are numerical examples to illustrate the suggested algorithm.