Global smooth stabilization of a class of feedforward systems under the framework of generalized homogeneity with monotone degrees

In this paper, based on the concept of generalized homogeneity with monotone degrees (HWMD), we develop a new design procedure to explicitly construct global stabilizers for a class of feedforward systems. The proposed controller design strategy has several new features. First, a series of positive constant gains instead of function gains are employed for a simpler controller construction. Second, the flexibility of HWMD provides a general framework to unify several existing results. Third, it is now possible to design continuously differentiable stabilizers for some feedforward systems, for which only continuous stabilizers were previously designed. Moreover, for feedforward systems with decreasing powers, the proposed approach will enable us to design a locally linear saturation control law which is easier to be implemented in practical applications.