786 citations · 2.4k across the 106 of their papers we have counts for
9 papers · 1 filter
Ordering Positive Definite Matrices
Cyrus Mostajeran, Rodolphe Sepulchre
We introduce new partial orders on the set of positive-definite matrices of dimension derived from the homogeneous geometry of induced by the natural transitive…
Analysis of Lur'e dominant systems in the frequency domain
F. A. Miranda-Villatoro, F. Forni, R. Sepulchre
Frequency domain analysis of linear time-invariant (LTI) systems in feedback with static nonlinearities is a classical and fruitful topic of nonlinear systems theory. We generalize…
Differential dissipativity theory for dominance analysis
Fulvio Forni, Rodolphe Sepulchre
High-dimensional systems that have a low-dimensional dominant behavior allow for model reduction and simplified analysis. We use differential analysis to formalize this important c…
A dissipativity theorem for p-dominant systems
Fulvio Forni, Rodolphe Sepulchre
We revisit the classical dissipativity theorem of linear-quadratic theory in a generalized framework where the quadratic storage is negative definite in a p-dimensional subspace an…
Robust modulation of integrate-and-fire models
Tomas Van Pottelbergh, Guillaume Drion, Rodolphe Sepulchre
By controlling the state of neuronal populations, neuromodulators ultimately affect behaviour. A key neuromodulation mechanism is the alteration of neuronal excitability via the mo…
Conal Distances Between Rational Spectral Densities
Giacomo Baggio, Augusto Ferrante, Rodolphe Sepulchre
The paper generalizes Thompson and Hilbert metric to the space of spectral densities. The resulting complete metric space has the differentiable structure of a Finsler manifold wit…