Analysis of Integral Input-to-State Stable time-delay systems in cascade

Abstract

Abstract We consider the cascade interconnection of two nonlinear time-delay systems, each of which being integral input-to-state stable (iISS). We provide an explicit growth rate condition on the dissipation rate of the driving system and the input rate of the driven system under which the overall cascade is globally asymptotically stable in the absence of inputs (0-GAS), and its solutions are bounded in response to any input with a suitable bounded-energy assumption.