Local asymptotic stabilization for a class of uncertain upper-triangular systems

Abstract

This paper considers local asymptotic stabilization of a class of uncertain upper-triangular systems. It shows that, by appropriately increasing the powers of the states in a linear controller, an uncertain upper-triangular system can be locally asymptotically stabilized. A nested nonlinear controller is designed by introducing the notion of homogeneity with strictly decreasing degrees. For the stability analysis, a common Lyapunov/Chetaev function is constructed and a necessary and sufficient condition for the local asymptotic stability is established.