Bypassing Disturbance Separability in Verifying Integral Input-to-State Stability of Cascade Systems

This paper proposes some variants of stability criteria for interconnected nonlinear systems which are not necessarily input-to-state stable. State-dependent weights introduced at disturbance ports remove disturbance separability assumptions made in previously known stability criteria for cascade systems. This paper put forward a unique idea of incorporating coupled weights into the formulation in order to deal with feedback interconnection of systems. The modifications require some uniformity in a feedback variable. Nevertheless, it is demonstrated that the coupled cascade formulation is sometimes far more effective than the integral input-to-state stable small-gain theorem which directly deal with feedback configurations.