Nonlinear small-gain theorems for large-scale time-delay systems

This paper presents nonlinear small-gain theorems for input-to-state stability and input-to-output stability properties of large-scale time-delay systems consisting of multiple subsystems based on Razumikhin-type techniques. A key strategy is to follow the spirit of the Razumikhin theorem and treat the state variables with delays as disturbances to the system in question. A consequence of this approach is that the problem of stability analysis for large-scale systems described by functional differential equations is converted into a more tractable one for state-delay-free systems with disturbances.