Stability analysis of a system coupled to a transport equation using integral inequalities*

We address the stability of a system of ordinary differential equations coupled with a transport partial differential equation, using a Lyapunov functional approach. This system can also be interpreted as a finite dimensional system subject to a state delay. Inspired from recent developments on time-delay systems, a novel method to assess stability of such a class of coupled systems is developed here. We will specifically take advantage of a polynomial approximation of the infinite dimensional state of the transport equation together with efficient integral inequalities in order to study the stability of the infinite dimensional system. The main result of this paper provides exponential stability conditions for the whole coupled system expressed in terms of linear matrix inequalities and the results are tested on academic examples.