• Corpus ID: 243860863

Structure-Preserving Linear Quadratic Gaussian Balanced Truncation for Port-Hamiltonian Descriptor Systems

  title={Structure-Preserving Linear Quadratic Gaussian Balanced Truncation for Port-Hamiltonian Descriptor Systems},
  author={Tobias Breiten and Philipp Schulze},
We present a new balancing-based structure-preserving model reduction technique for linear port-Hamiltonian descriptor systems. The proposed method relies on a modification of a set of two dual generalized algebraic Riccati equations that arise in the context of linear quadratic Gaussian balanced truncation for differential algebraic systems. We derive an a priori error bound with respect to a right coprime factorization of the underlying transfer function thereby allowing for an estimate with… 

Figures from this paper

Structure preserving model order reduction of port-Hamiltonian systems
This work proposes a structure-preserving model reduction method for linear, time-invariant port-Hamiltonian systems. We show that a low order system of the same type can be constructed which
The difference between port-Hamiltonian, passive and positive real descriptor systems
The relation between passive and positive real systems has been extensively studied in the literature. In this paper, we study their connection to the more recently used notion of port-Hamiltonian


Error bounds for port-Hamiltonian model and controller reduction based on system balancing
Structured backward errors for eigenvalues of linear port-Hamiltonian descriptor systems
A backward error analysis is performed and it is shown that for matrix pencils associated with port-Hamiltonian descriptor systems and a given computed eigenstructure with the correct symmetry structure there always exists a nearby port- Hamiltonian descriptor system with exactly that eigenStructure.
Structure-preserving Interpolatory Model Reduction for Port-Hamiltonian Differential-Algebraic Systems
This work focuses on linear time-invariant systems and presents a systematic treatment of a variety of model classes that include combinations of index-$1$ and index-$2$ systems, describing in particular how constraints may be represented in the transfer function and then preserved with interpolatory methods.
Passivity preserving model reduction via spectral factorization
On Linear-Quadratic Optimal Control and Robustness of Differential-Algebraic Systems
This thesis considers the linear-quadratic optimal control problem for differentialalgebraic equations. In this first part we present a complete theoretical analysis of this problem. The basis is a
Balanced Realization and Model Order Reduction for Port-Hamiltonian Systems
This paper is concerned with nonlinear model order reduction for electro-mechanical systems described by port-Hamiltonian formulae. A novel weighted balacend realization and model order reduction
Parametric Model Order Reduction of Port-Hamiltonian Systems by Matrix Interpolation
A new weighted matrix interpolation of locally reduced models is introduced in order to preserve the port-Hamiltonian structure, which guarantees the passivity and stability of the interpolated system.