Global adaptive stabilisation of feedforward systems by smooth output feedback

The authors address the problem of global output-feedback stabilisation for a class of feedforward nonlinear systems. The system satisfies linear growth condition with an unknown growth rate. Using the dynamic gain scaling technique and introducing a new adaptive law, it is proved that global adaptive stabilisation of the feedforward systems can be achieved by smooth output feedback. The gain matrices are only required to satisfy the Hurwitz condition, which makes the control law very easy to implement. Moreover, the authors show that for feedforward systems and low triangular systems with unknown linear growth rate, global adaptive stabilisation can be handled in a unifying framework, that is, the observer and the controller can be designed in a same structure just with two different adaptive laws for the dynamic gain, respectively.