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 nonlinear 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 nonlinear 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 the backstepping manner, which can be recognized as partial state feedback for the composite system as it uses only the states of the linear subsystem.