Balancing for Nonlinear Differential-Algebraic Control Systems

In this paper, we develop a balancing theory for nonlinear differential-algebraic control systems. We exploit the maximally controlled invariant submanifold to define the controllability and observability functions and to provide a balanced realization. We also construct a reduced-order model based on truncation of states which also preserves the constraints associated with the original system. Finally, we illustrate the results with an example.