Lyapunov-Razumikhin and Lyapunov-Krasovskii theorems for interconnected ISS time-delay systems
نویسندگان
چکیده
We consider an arbitrary number of interconnected nonlinear systems with time-delays and investigate them in view of input-to-state stability (ISS). The useful tools for single time-delay systems, the ISS Lyapunov-Razumikhin functions and ISS Lyapunov-Krasovskii functionals are redefined and applied to interconnected systems. By the help of a smallgain condition we prove that the whole system with time-delays has the ISS property, if each subsystem has an ISS LyapunovRazumikhin function or ISS Lyapunov-Krasovskii functional. Furthermore we construct the ISS Lyapunov-Razumikhin (Krasovskii) function(al) and the corresponding gains of the whole system.
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