Control and Calculation of the H2-norm for Singular and/or Fractional Models

Abstract

This work emphasizes the development of a new approach for computing the impulse response energy, known, also, as the H2-norm, for a certain class of fractional linear models. The main concept of this new approach is the use of the state-space realization consisting of parameters that are extracted from the fractional-order transfer function and then a transformation other than those proposed in the literature of the parahermitian matrix which let it invariant. Finally, the general expression of the H2-norm is derived thanks to some concepts and some conditions set out. Numerical results on both first-order and second-order fractional transfer functions with real and complex parameters illustrate the performance of the proposed approach. Through the promising results, this approach opens great perspectives on theoretical developments that can handle numerous algorithms responding to diverse needs.