Stabilization and adaptive L2-disturbance attenuation control of a class of nonlinear descriptor systems

This paper studies the stabilization, L
₂
-disturbance attenuation control and adaptive L
₂
-disturbance attenuation control of a class of nonlinear descriptor systems, and presents a number of new results on the control designs. First, under a suitable state feedback, two sufficient conditions of impulse-free are given for the resulted closed-loop system. Then, the stabilization problem is discussed for the nonlinear descriptor system, and a stabilization control design procedure is presented, based on which an admissible L
₂
-disturbance attenuation controller and an admissible adaptive L
₂
-disturbance attenuation controller are designed for the system with external disturbances and/or parametric uncertainties. Simulation results on a nonlinear descriptor circuit system show the efficiency of the controllers proposed in this paper.