Semi-Global Stabilization of a Class of Cascade Systems by a Separate Design Approach

The semi-global stabilization of a class of cascade systems (e.g., partially linear composite systems) is investigated via partial state feedback. The system comprises a non-linear subsystem with a cross-term and a linear subsystem in the Byrnes-Isidori normal form. The cross-term that involves any two consecutive states of chains of integrators is incorporated into the non-linear subsystem. Based on the established lemma for separate design, the semi-global stabilization problem for the entire composite system is reduced to stabilizing its linear subsystem subject to non-peaking constraints on the consecutive states. To address the later problem, a linear low- and high-gain feedback law is developed in a backstepping manner, which can be recognized as partial state feedback for the composite system as it uses only the states of the linear subsystem.