An Immersion and Invariance Algorithm for a Differential Algebraic System

A stability result based on the Immersion and Invariance control strategy is derived for a class of systems described by differential equations with algebraic constraints. The result is then applied to synthesize a stabilizing control law for a two machine electrical power system with a controllable series capacitor (CSC). The dynamics of the two-machine system is given by differential equations and the active power balance at the load buses is given by algebraic equations. The CSC dynamics is described by a first order differential equation.