Practical output tracking of nonlinear systems with uncontrollable unstable linearization

The paper focuses on the problem of having the output of nonlinear systems track a prescribed C¹ reference signal. It is proved that, under mild assumptions, global practical output tracking is achievable by smooth state feedback, although asymptotic output tracking is usually not possible (even locally) because the linearized system has uncontrollable modes whose eigenvalues are on the right half plane. Smooth feedback controllers which solve the problem of global practical output tracking are explicitly constructed, based on a modified ´adding a power integrator´ approach. This feedback design method also leads to solutions to challenging benchmark control problems, including practical output tracking of an underactuated unstable two degrees of freedom mechanical system