Martine Olivi

Adam Cooman, Fabien Seyfert, Martine Olivi et al.

Performing a stability analysis during the design of any electronic circuit is critical to guarantee its correct operation. A closed-loop stability analysis can be performed by analysing the impedance presented by the circuit at a well-chosen node without internal access to the simulator. If any of the poles of this impedance lie in the complex right half-plane, the circuit is unstable. The classic way to detect unstable poles is to fit a rational model on the impedance. In this paper, a projection-based method is proposed which splits the impedance into a stable and an unstable part by projecting on an orthogonal basis of stable and unstable functions. When the unstable part lies significantly above the interpolation error of the method, the circuit is considered unstable. Working with a projection provides one, at small cost, with a first appraisal of the unstable part of the system. Both small-signal and large-signal stability analysis can be performed with this projection-based method. In the small-signal case, a low-order rational approximation can be fitted on the unstable part to find the location of the unstable poles.

Laurent Baratchart, Per Enqvist, Andrea Gombani et al.

We consider the symmetric Darlington synthesis of a p x p rational symmetric Schur function S with the constraint that the extension is of size 2p x 2p. Under the assumption that S is strictly contractive in at least one point of the imaginary axis, we determine the minimal McMillan degree of the extension. In particular, we show that it is generically given by the number of zeros of odd multiplicity of I-SS*. A constructive characterization of all such extensions is provided in terms of a symmetric realization of S and of the outer spectral factor of I-SS*. The authors's motivation for the problem stems from Surface Acoustic Wave filters where physical constraints on the electro-acoustic scattering matrix naturally raise this mathematical issue.

Pauline Kergus, Martine Olivi, Charles Poussot-Vassal et al.

The choice of a reference model in data-driven control techniques is a critical step. Indeed, it should represent the desired closed-loop performances and be achievable by the plant at the same time. In this paper, we propose a method to build such a reference model, both reproducible by the system and having a desired behaviour. It is applicable to Linear Time-Invariant (LTI) monovariable systems and relies on the estimation of the plant's instabilities through a data-driven stability analysis technique. The L-DDC (Loewner Data Driven Control) algorithm is used to illustrate the impact of the choice of the reference model on the control design process. Finally, the proposed choice of specifications allows to use a controller validation technique based on the small-gain theorem.