# Jean-Baptiste Pomet - Inria Sophia, McTAO - Keywords: Stability analysis, delay systems, nonlinear circuits

Nonlinear hyperfrequency amplifiers contain nonlinear active components and lines, that can be seen as linear infinite dimensional systems inducing delays that cannot be neglected at high frequencies. Computer assisted design tools are extensively used. They provide frequency responses but fail to provide a reliable estimation of their stability, and this stability is crucial because an unstable response will not be observed in practice and the engineer needs to have this information between building the actual device.

We shall present the models of such devices, and the current methods to compute the response to a given periodic signal to be amplified (this is a periodic solution of a periodically forced infinite dimensional dynamical system) as well as the frequency response of an input-output system associated to the linearization around this periodic solution.

The goal of the talk is to present the ideas and preliminary results that on the one hand allow to deduce stability of this time-varying linear system from that frequency response and on the other hand provide a relationship between this stability and the internal stability of the actual nonlinear circuit. The first point resorts from harmonic analysis and perturbation of linear operators. The second one from nonlinear infinite dimensional dynamics and ad'hoc linearization.

This is an ongoing project at Inria, in teams MCTAO and APICS.