Nonlinear multi-index design of a differential algebraic power system

A nonlinear multi-index control (NMIC) method for studying the stability of a differential algebraic (DA) system is presented. In this method, the output function is the linear combination of the state vectors and algebraic variables. The nonlinear control law was designed in a linear space by means of homeomorphic transformation. The relative degree was defined in a special DA system, which can be accepted by ordinary DA system in future research work. As an interesting application, it is found that the controlled single machine infinite system (SMIS) designed using this method shows satisfactory dynamic behavior and excellent steady state accuracy.