On computation of H∞ norm for commensurate fractional order systems

Abstract

This paper tackles the problem of H-infinity (H∞) norm computation for a commensurate Fractional Order System (FOS). First, H∞ norm definition is given for FOS and Hamiltonian matrix of a FOS is computed. Two methods based on this Hamiltonian matrix are then proposed to compute the FOS H∞ norm: one based on a dichotomy algorithm and another one on LMI conditions. The LMI conditions are based on the Generalized LMI characterization of axes in the complex plane on which the Hamiltonian matrix eigenvalues must not appear to ensure a FOS norm less than predefined value. The accuracy of the proposed methods is proved on the computation of the modulus margin of a CRONE passive car suspension.