Dynamics of delayed switched nonlinear systems with applications to cascade systems

This paper addresses the dynamic properties of a class of continuous-time switched nonlinear systems with perturbations and delays. With the assumption that the nominal system is exponentially stable, it is shown that the trajectory of the perturbed system exponentially decays to or asymptotically approaches origin provided that the perturbation exponentially decays to or asymptotically approaches origin. These properties are then applied to cascade systems for their stability analysis. It is proven that a delayed switched nonlinear cascade system is exponentially stable if and only if all subsystems obtained from the cascade system by deleting the coupling terms are exponentially stable. A sufficient condition ensuring asymptotic stability of a cascade system is also proposed.