Further results on Lyapunov-Krasovskii functionals via nonlinear small-gain conditions for interconnected retarded iISS systems

This paper presents further results on the problem of establishing stability of retarded nonlinear interconnected systems comprising integral input-to-state stable subsystems. It is shown that the stability of the interconnected systems with respect to external signals can be verified by constructing Lyapunov-Krasovskii functionals explicitly whenever small-gain type conditions are satisfied. The primary result [12] is generalized in two aspects. One is to introduce a new flexibility in constructing Lyapunov-Krasovskii functionals to deal with distributed delays more effectively. The other is to cover systems involving time-varying delays in interconnecting channels.