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,
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,
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,
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.