Balanced truncation model reduction for semidiscretized Stokes equation

We discuss model reduction of linear continuous-time descriptor systems that arise in the control of semidiscretized Stokes equations. Balanced truncation model reduction methods for descriptor systems are presented. These methods are closely related to the proper and improper controllability and observability Gramians and Hankel singular values of descriptor systems. The Gramians can be computed by solving projected generalized Lyapunov equations. Important properties of the balanced truncation approach are that the asymptotic stability is preserved in the reduced order system and there is an a priori bound on the approximation error. We demonstrate the application of balanced truncation model reduction to the semidiscretized Stokes equation.