I will first recall some results on how to achieve consensus for well known classes of systems, like the celebrated Cucker-Smale or Hegselmann-Krause models. When the systems are symmetric, convergence to consensus is classically established by proving, for instance, that the usual variance is an exponentially decreasing Lyapunov function: this is a "L^2 theory". When the systems are not...

In this presentation, we will be interested in an inverse problem set on a tree shaped network where each edge behaves according to the wave equation with potential, external nodes have Dirichlet boundary conditions and internal nodes follow the Kirchoff law. The main goal is the reconstruction of the potential everywhere on the network, from the Neumann boundary measurements at all but one...

We discuss infinite-dimensional forward complete dynamical systems which are subject to uncertainties, representing switching parameters or external disturbances. We characterize the uniform (with respect to uncertainties) local, semi-global, and global exponential stability, in terms of coercive and non-coercive Lyapunov functionals. We illustrate the potential usefulness of the result...