Nonlinear composite control of a class of nominally linear singularly perturbed uncertain systems

The conditions that allow the construction of a composite control for the practical stabilisation of a singularly perturbed uncertain system have been analysed. Even though the system has been considered nominally linear, the presence of the uncertainties couples the fast and the slow dynamics of the system and, in consequence, the controller must contain a nonlinear term that allows the separate design of the fast and the slow controllers. It has been found that the feedback gains of the slow variable, besides having a lower bound (as is usual in the control of uncertain systems), also possess an upper bound that depends mainly on the structural coupling between the slow and the fast parts of the system. This upper bound prevents the variables which have been con sidered as having slow dynamics from becoming fast under the action of a high gain feedback.