Global asymptotic stabilization of nonminimum phase nonlinear systems via extended backstepping

We address the problem of global asymptotic stabilization for a single-input single-output nonlinear system that may not be minimum phase. To solve this problem, we introduce a set of invariant manifolds which have hierarchical structure. We transform the plant repeatedly by using this set of invariant manifolds. Under the linear growth condition and some additional assumptions, global asymptotic stabilization is achieved by applying a variable-gain state feedback law to the obtained system.