Input-output and input-to-state stabilization of cascaded nonlinear systems

In this paper we provide a rather complete set of passivity sufficiency conditions that give asymptotic stabilizability of nonlinear cascades of driving-driven systems. Moreover, we analyze the input-output and input-to-state stability properties of existing stabilization schemes. This allows us to derive the weakest passivity assumption on the driving system that give the required stability. In addition, we state stability properties of different versions of strict passivity and illustrate their connections through some examples.