Generalized homogeneity with monotone degree and smooth stabilization for a class of feedforward systems

In this paper, by integrating the generalized homogeneity with monotone degrees (HWMD) with the top-bottom/bottom-top design strategy, we develop a new design procedure which enables us to explicitly construct global stabilizers for a class of feedforward systems. The proposed new control design strategy has several new features. First, a series of positive constant gains instead of positive function gains are updated to overcome the disadvantage caused by the variety of homogenous degrees. Second, the flexibility of HWMD provides a general framework to unify several existing results. Moreover, now it is possible to design continuously differentiable stabilizers for some feedforward systems for which only continuous stabilizers were previously designed.