H∞H∞ analysis and control of commensurate fractional order systems

• LMI conditions for computing L∞ and H∞ norms of fractional order models are proposed.
• They involve fewer variables than the ones available in the literature.
• Using these conditions, LMI pseudo state feedback synthesis conditions are derived.
• Results are used to design a controller minimizing a bridge seismic response.
• Seismic isolation is performed through elastomeric bearings and semiactive dampers.

This paper addresses the problem of the H∞H∞ control of commensurate Fractional Order Systems (FOS). Along the lines of recent work on H∞H∞ norm computation for FOS, new extensions of the L∞L∞ and H∞H∞ bounded real lemmas to FOS are given after stating the differences between those two norms. An H∞H∞ state feedback control method based on the corresponding bounded real lemma is then proposed. The efficiency of this method is evaluated on numerical examples.