Backstepping stabilization control for MIMO nonlinear differential-algebraic equations subsystem and its applications

For MIMO nonlinear differential-algebraic equations (DAE) subsystem, the Backstepping stabilization control method is studied and the results are applied to the decentralized control of power system. The concept of vector relative order for MIMO nonlinear DAE subsystem is put forward. If the vector relative order exists, then the subsystem can be transformed equivalently by a diffeomorphism and a feedback. Next the Backstepping method is used to design the stabilization controller, through which the asymptotic stability of the whole closed-loop system is obtained. Finally the synchronous generator excitation and valve control is studied, and the simulation results illustrate the utility of the method proposed in this paper.