In this paper, a nonlinear control-system design framework predicated on a
hierarchical switching controller architecture parameterized over a set of
moving system equilibria is developed. Specifically, using equilibria-depen
dent Lyapunov functions, a hierarchical nonlinear control strategy is devel
oped that stabilizes a given nonlinear system by stabilizing a collection o
f nonlinear controlled subsystems. The switching nonlinear controller archi
tecture is designed based on a generalized lower semicontinuous Lyapunov fu
nction obtained by minimizing a potential function over a given switching s
et induced by the parameterized system equilibria. The proposed framework p
rovides a rigorous alternative to designing gain-scheduled feedback control
lers and guarantees local and global closed-loop system stability for gener
al nonlinear systems.