C. Poussot-Vassal

V. Bellet, C. Poussot-Vassal, C. Pagetti et al.

Traditionally, the delay margin of a looped system is computed by considering both the controller and system representations that evolve in the same space (e.g. either continuous or discrete-time). However, as in practice the system is continuous and the controller is mostly embedded in a computer, the looped - controller / system pair - model is hybrid. As a consequence, the computed delay margin might vary with respect to the continuous (or discrete one). This paper proposes a novel approach to compute the exact delay margin of hybrid systems, and more specifically, when a discrete-time controller is looped with a continuous-time system. The main interest is then to provide the practitioners with a way to select the appropriate discretization technique for maximizing the delay margin and to be able to exactly evaluate the delay margin before implementation on target. The main idea is to approximate the discrete-time controller with an equivalent continuous-time one (often with higher order) and to exploit the classical continuous-time frequency-based analysis strategies.

C. Poussot-Vassal

This paper proposes an simple but yet effective approach to structured parametric controller design in a linear fractional form. The main contribution consists in using structured $\mathcal{H}_\infty$ oriented optimization tools in an original manner to either (i) construct a parametric controller or (ii) a family of controllers with varying performances. Practical and numerical issues are also discussed to provide readers and practitioners a simple way to deploy the proposed process. The overall approach is illustrated through two numerical academical (but still complex) examples illustrating two applications: first, a parametric controller design adapted to a parameter dependent model of a clamped beam and, second, a controller with parameter dependent performance applied on a building model.

A. C. Antoulas, I. V. Gosea, C. Poussot-Vassal

This work shows that for rational multivariate functions, the Kolmogorov Superposition Theorem (KST) involves several single-variable functions, which can be written down by inspection. In other words, no computation is required for decoupling the variables of multivariate rational functions. The key tool for this development is the Loewner Framework for multivariate functions. Applications of this result involve approximating multivariate non-rational functions by low-complexity multivariate rational and polynomial functions.

I. Pontes Duff, C. Poussot-Vassal, C. Seren

In this paper, the realization-free model approximation problem, as stated in \cite{mayo2007framework,beattie2012realization}, is revisited in the case where the interpolating model might be time-delay dependent. To this aim, the Loewner framework, initially settled for delay-free realization, is firstly generalized to the single delay case. Secondly, the (infinite) model approximation $\mathcal{H}_2$ optimality conditions are established through the use of the Lambert functions. Finally, a numerically effective iterative scheme, named \textbf{dTF-IRKA}, similar to the \textbf{TF-IRKA} \cite{beattie2012realization}, is proposed to reach a part of the aforementioned optimality conditions. The proposed method validity and interest are assessed on different numerical examples.