Smooth stabilization of nonlinear control systems

Abstract

This paper provides the framework for a general approach for constructing smooth stabilizing feedback for smooth nonlinear systems when it is possible to construct such a feedback. Algorithms for determining the local smooth asymptotic stabilizability of two specific classes of smooth nonlinear control systems are developed. These two classes of systems are identified with systems whose linearizations possess either one zero eigenvalue or a pair of purely imaginary eigenvalues. The local stabilizability of any critical nonlinear system in either of these classes may be tested once the system's linearization is block diagonalized with respect to the critical and stable eigenvalues.