Non-Standard Dissipative Operators

            Like pseudo-differential operators of diffusive type in continuous time, diffusive filters in discrete time have been introduced for the fractional difference filter and for other discretizations of fractional integrals. The impulse response of diffusive filters can be decomposed on a continuous family of geometric sequences with a decreasing weight. Using this diffusive realization, in the sense of systems theory, it helps transforming a non-local in time difference equation into a first order difference equation on an infinite-dimensional state-space, endowed with a Hilbert structure, which allows for positivity, dissipativity, asymptotic and stability analysis.

List of  Publications

     Gabriel Dauphin. PHD. Application des représentations diffusives à temps discret. Traitement du signal et de l’image. Télécom ParisTech, 2001. Français


      G. Dauphin and D. Matignon. Positivity and Dissipativity of Oscillating Diffusive Filters, Application to the Stability of Coupled Systems. In Proceeding of Mathematical Theory of Networks and Systems symposium, 10 pages, Notre Dame, Indiana, USA, 2002. MTNS'02.


      G. Dauphin and D. Matignon. Application of Diffusive Representations to Discretized Fractional Systems: Stability, Positivity and Simulations Issues. In Proceeding of European Control Conference, pages 1490-1495, Porto, Portugal, September 2001. ECC'01.

      G. Dauphin, D. Heleschewitz and D. Matignon. Extended Diffusive Representations and Application to Non-Standard Oscillators. In Proceeding of Mathematical Theory of Networks and Systems symposium, 10 pages, Perpignan, France, June 2000. MTNS'00.

      G. Dauphin and D. Matignon. Premiers résultats sur les représentations diffusives à temps discret et application aux filtres ARFIMA. In Proceeding of Journées Doctorales d'Automatique, pages 45-48, Nancy, France, septembre 1999. GDR AUTOMATIQUE.

      G. Dauphin and D. Matignon. Stabilité interne d'un système couplé à temps discret, formé d'un oscillateur et d'un filtre diffusif dissipatif. In Journéées Doctorales d'Automatique, pages 189-194, Toulouse, France, septembre 2001. GDR AUTOMATIQUE.