L_2 Gain Disturbance Attenuation for Nonlinear Singularly Perturbed Systems

The problem of L₂ gain disturbance attenuation is considered for a class of nonlinear singularly perturbed system. Based on Lyapunov argument and backstepping design technique, a state feedback controller is constructed for the slow-subsystem which renders a full closed-loop system internally stable with bounded L₂ gain from exogenous input to output. No Hamilton-Jacobi equation is needed for the controller design. A simulation example shows the feasibility and effectiveness of the conclusion.