Abstract: The notion of control Lyapunov functions(CLF), originated from relaxed controls, is newly understood as the characterization of zero-state detectability property, thus the difference between the Sontag-type control[1] and the passivity-based controller is clarified accordingly. Then, based on a CLF under appropriate conditions, a Sontag-type stabilizer is designed for a class of typical cascaded systems which have ever been stabilized by passivity-based controllers. Furthermore, based on an input-to-state stable CLF under appropriate conditions, a Sontag-type input-to-state stabilizer is designed for this kind of cascaded systems with perturbation.