Stabilization of a class of nonlinear systems with ill-defined relative degree

Many industrial systems have a so-called “ill-defined relative degree”, including for instance the overhead crane. A practical approach to stabilizing such systems is presented. Canceling the nonlinearities by system inversion is infeasible in these systems. However, a control can often be selected to achieve perfect cancellation of the nonlinearities when the states are large. If the system is closed-loop observable from measurements of the control input coefficient-function, then it is shown that such a control ensures that the states are uniformly ultimately bounded. These results indicate an important connection between the control of ill-defined relative degree systems and their observability through a special output. The assumptions on the system are simple and often easy to verify. This approach is shown to be effective even when the approximate linearization techniques popular in literature fail