Section: New Results

Neutral systems and integral equations

Participants : Frédéric Mazenc [correspondent] , Hiroshi Ito [Kyushu Institute of Technology] , Pierdomenico Pepe [Univ. of L'Aquila] .

1) For nonlinear systems with delay of neutral type, we developped a new technique of stability and robustness analysis. It relies on the construction of functionals which make it possible to establish estimates of the solutions different from, but very similar to, estimates of ISS or iISS type. These functionals are themselves different from, but very similar to, ISS or iISS Lyapunov-Krasovskii functionals. The approach applies to systems which do not have a globally Lipschitz vector field and are not necessarily locally exponentially stable. We apply this technique to carry out a backstepping design of stabilizing control laws for a family of neutral nonlinear systems [21] .

2) In a second paper [57] , we extended the previous results to the problem of deriving stability and stabilizability conditions for nonlinear systems with delay interconnected with an integral equation via the construction of a Lyapunov-Krasovskii functional.