Global asymptotic output tracking of nonlinear second-order systems with power integrators

This brief considers the problem of designing controllers to make the output of a power-integrator planar system globally asymptotically track the reference signal generated by a power-integrator exosystem. A necessary and sufficient condition on the powers of the integrators is identified for the solvability of the problem. In the higher order case, the tracking controllers are explicitly constructed by employing the tool of adding a power integrator. In the lower order case, a weak version of adding a power integrator technique is developed to enable us to construct tracking controllers.