A General Class of Control Lyapunov Functions and Sampled-Data Stabilization

Several important contributions toward sampled-data and hybrid feedback stabilization have appeared in the literature. This article extends recent results by second author concerning sampled-data feedback stabilization for affine in the control of nonlinear systems with a nonzero drift term, under the presence of a generalized control Lyapunov function associated with appropriate Lie algebraic hypotheses concerning the dynamics of the system. The main results of this article constitute a generalization of the well-known “Artstein-Sontag” theorem on asymptotic stabilization by means of an almost smooth feedback controller. The analysis is limited to the affine single-input nonlinear systems with nonzero drift term; however, the results can easily be extended to the multi-input case. An illustrative example of the derived results is included.