Section: New Results

Analysis of neutral systems

Participants : Frederic Mazenc, Hiroshi Ito [Kyushu Institute of Technology] .

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 [22] , [45] .

2) We extended the previous result to the problem of deriving the iISS property for dynamical networks with neutral, retarded and communication delay [41] .