Robust stabilization of a class of nonlinear descriptor systems

This paper studies the stabilization and H_∞ control of a class of nonlinear descriptor systems, and presents many new results on the control designs by using the dissipative matrix method. Based on the structural characteristic of the nonlinear descriptor system, an equivalent nonlinear dissipative differential-algebraic system is obtained by a suitable state feedback, and two sufficient conditions of impulse-free are given for the resulted closed-loop descriptor system. With the feedback dissipative form, the stabilization problem is then discussed for the nonlinear descriptor system, and a stabilization control design procedure is presented, based on which an admissible H_∞ controller is designed for the system with external disturbances. Simulation results on nonlinear descriptor circuit systems show the efficiency of the controllers proposed in this paper.