Gain scheduling control of nonlinear singularly perturbed time-varying systems with derivative information

In this paper, we analyse the ultimate boundedness of nonlinear singularly perturbed time-varying systems and propose a control law using gain scheduling where the slow state and the exogenous signals are used as scheduling variables. In our control scheme, we have some flexibility in selecting the slow manifold of the system. Moreover, the derivative information can be properly engaged to manipulate the size of ultimate bound in tracking error of the controlled system.