On differential input-to-state stability

Recently, a Finsler-Lyapunov function is provided for incremental stability analysis in the contraction framework. In this paper, by using this Finsler-Lyapunov function, we study differential input-to-state stability (ISS). Especially, we give sufficient conditions for differential ISS and differential integral ISS. An example demonstrates that a differential ISS condition can be used for synchronization analysis of a coupled oscillator.