Robust semiglobally practical stabilization for nonlinear singularly perturbed systems

In this work, the problem of semiglobally practical stabilization is considered for nonlinear singularly perturbed systems with unknown parameters. The composite Lyapunov function for the full systems is established by both that of the slow subsystem and the boundary layer system. A state feedback control law for the linear part of the slow subsystem and boundary layer system is proposed which renders the whole closed-loop system semiglobally stable. The upper bound expression of ε is given to obtain the condition of asymptotic stability for the system. A simulation example is given to demonstrate the effectiveness and feasibility of the controller.