Uniform global practical asymptotic stability for time-varying cascaded systems

This paper aims to give sufficient conditions for a cascade composed of nonlinear time-varying systems that are uniformly globally practically asymptotically stable (UGPAS) to be UGPAS. These conditions are expressed as relations between the Lyapunov function of the driven subsystem and the interconnection term. Our results generalise previous theorems that establish the uniform global asymptotic stability of cascades and its application is illustrated by characterising the effect of smoothing control laws in disturbance rejection.