Non-Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization

Without imposing any growth condition, we prove that every chain of odd pow er integrators perturbed by a CL triangular vector field is globally stabil izable via non-Lipschitz continuous state feedback, although it is not stab ilizable, even locally, by any smooth state feedback because the Jacobian l inearization may have uncontrollable modes whose eigenvalues are on the rig ht half-plane. The proof is constructive and accomplished by developing a m achinery - adding a power integrator - that enables one to explicitly desig n a C-0 globally stabilizing feedback law as well as a C-1 control Lyapunov function which is positive definite and proper. (C) 2001 Elsevier Science B.V. All rights reserved.