Characterizations of cascaded systems with monomial interconnections and GES inputs

The stability characteristics for a class of cascaded nonlinear systems with mononomial interconnections is investigated. Conditions are developed to identify regions of stability for the system and to demonstrate the existence of finite-time escape trajectories, in the presence of exponentially stable system inputs. The main result is the complete characterization of the system behaviour through the analysis of the stability properties of exact solutions to various special cases of the system, and additional Lyapunov stability techniques.