We generalize an alternating direction implicit method and the Smith method for large-scale projected generalized Lyapunov equations. Such equations arise in model reduction of descriptor systems.â€¦ (More)

In this paper we give a survey on balanced truncation model order reduction for linear time-invariant continuous-time systems in descriptor form. We first give a brief overview of the basic conceptsâ€¦ (More)

Model reduction is of fundamental importance in many control applications. We consider model reduction methods for linear time-invariant continuous-time descriptor systems. These methods are based onâ€¦ (More)

We consider the numerical solution of projected Lyapunov equations using Krylov subspace iterative methods. Such equations play a fundamental role in balanced truncation model reduction of descriptorâ€¦ (More)

We present generalizations of the impulse and frequency responses as well as convolution and Hankel operators for continuous-time and discrete-time descriptor systems. Some norms for descriptorâ€¦ (More)

In this paper we discuss the numerical solution of projected generalized Lyapunov equations using the matrix sign function method. Such equations arise in stability analysis and control problems forâ€¦ (More)

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 descriptorâ€¦ (More)

We present a passivity-preserving balanced truncation model reduction method for differential-algebraic equations arising in circuit simulation. This method is based on balancing the solutions ofâ€¦ (More)