Asymptotic stabilization of nonlinear systems via sign-indefinite damping injection

The problem of asymptotic stabilization of nonlinear, “double integrator”, open-loop stable systems via sign-indefinite damping injection is considered in this paper. A constructive procedure to reduce the problem to the solution of a set of partial differential equations is presented. Particular emphasis is given to mechanical systems, for which it is shown that the proposed approach obviates the usual detectability assumption needed to conclude asymptotic stability via LaSalle´s invariance principle.