Séminaire DISC : Recent developments on the stability analysis of time-delay systems and perspectives

Invité : Alexandre Seuret (LAAS)

In this talk, a review of the recent developments on time-delay is proposed. This class of systems appears in many applications areas such as in Engineering, Biology, Communications, Traffic management among many others.

One of the particularities of time-delay systems compared to classical systems studied in Automatic Control arises from its infinite dimensional nature. Indeed, the state of such systems is a function collecting the past values of the instantaneous vector over the delay interval. Therefore, in order to characterize stability using a Lyapunov argument, one has to define a Lyapunov functionals depending on this infinite dimensional state vector. In the last two decades, many researchers have considered this problem and have provided tractable stability conditions expressed in terms of Linear Matrix Inequality.
A recent method based on efficient integral inequality has demonstrated its potential and has led to a relevant tradeoff between conservatism and complexity of the resulting conditions.

At the end of this presentation, an extension of this stability analysis to a larger class of infinite dimensional systems is discussed. More particularly, the stability problem of coupled ODE - (transport/heat/wave) PDE is addressed.