ABSTRACT
In this chapter, we will develop a balancing based model reduction method for a class of first-order unstable index 2 descriptor systems. For this purpose, we modify the low-rank ADI iteration for Lyapunov equations to deal with the index 2 structure of the underlying descriptor system efficiently in an implicit way. The chapter also discusses the way of constricting the feedback stablization of the original model from the reduced system. The resulting algorithm is tested for model reduction of the linearized Navier stokes system. Numerical results are discussed for confirming the efficiency of the proposed method.
