# Error bounds for port-Hamiltonian model and controller reduction based on system balancing

@article{Breiten2022ErrorBF, title={Error bounds for port-Hamiltonian model and controller reduction based on system balancing}, author={Tobias Breiten and Riccardo Morandin and Philipp Schulze}, journal={Comput. Math. Appl.}, year={2022}, volume={116}, pages={100-115} }

## 7 Citations

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

- Mathematics, Computer ScienceArXiv
- 2021

A novel procedure that is based on a recently introduced Kalman–Yakubovich–Popov inequality for descriptor systems is provided, demonstrating how the quality of reduced-order models can significantly be improved by first computing an extremal solution to this inequality.

Ju n 20 22 Structure-Preserving H ∞ Control for Port-Hamiltonian Systems June 20 , 2022

- Mathematics
- 2022

We study H∞ control design for linear time-invariant port-Hamiltonian systems. By a modification of the two central algebraic Riccati equations, we ensure that the resulting controller will be…

Error bounds for model reduction of feedback-controlled linear stochastic dynamics on Hilbert spaces

- Mathematics, Computer ScienceStochastic Processes and their Applications
- 2022

Port-Hamiltonian Dynamic Mode Decomposition

- MathematicsArXiv
- 2022

. We present a novel physics-informed system identiﬁcation method to construct a passive linear time-invariant system. In more detail, for a given quadratic energy functional, measurements of the…

Passivity preserving model reduction via spectral factorization

- Computer Science, MathematicsAutom.
- 2022

Port-Hamiltonian Fluid-Structure Interaction Modeling and Structure-Preserving Model Order Reduction of a Classical Guitar

- PhysicsArXiv
- 2022

A fluid-structure interaction model in a port-Hamiltonian representation is derived for a classical guitar. We combine the laws of continuum mechanics for solids and fluids within a unified…

On the sample complexity of stabilizing linear dynamical systems from data

- Computer Science, MathematicsArXiv
- 2022

If a linear dynamical system has dimension (McMillan degree) n, then there always exist n states from which a stabilizing feedback controller can be constructed, independent of the dimension of the representation of the observed states and the number of inputs.

## References

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Structure preserving reduction of port hamiltonian system using a modified LQG method

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This paper proposes a controller reduction method for the port Hamiltonian system by using a modified LQG method. We first use the LQG method to design two passive type controllers which are…

Structure-preserving discretization for port-Hamiltonian descriptor systems

- Mathematics2019 IEEE 58th Conference on Decision and Control (CDC)
- 2019

This work extends the modeling framework of port-Hamiltonian descriptor systems to include under- and overdetermined systems and arbitrary differentiable Hamiltonian functions, and shows that this structure is invariant under a wide class of nonlinear transformations, and can be naturally modularized, making it adequate for automated modeling.

Energy-Preserving and Passivity-Consistent Numerical Discretization of Port-Hamiltonian Systems

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This paper designs discrete port-Hamiltonian systems systematically in two different ways, by applying discrete gradient methods and splitting methods respectively, and results are encouraging when compared to relevant existing integrators of identical order.

Passivity and Structure Preserving Order Reduction of Linear Port-Hamiltonian Systems Using Krylov Subspaces

- MathematicsEur. J. Control
- 2010

In this paper, a new structure-preserving scheme for the reduction of linear port-Hamiltonian systems with dissipation using Krylov subspaces is presented. It is shown how to choose the projection…

Stability Radii for Linear Hamiltonian Systems with Dissipation Under Structure-Preserving Perturbations

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- 2016

It is shown that under structure-preserving perturbations the asymptotical stability of a DH system is much more robust than under general perturbation, since the distance to instability can be much larger when struc...

Structure-preserving tangential interpolation for model reduction of port-Hamiltonian systems

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- 2012

Truncated balanced realization of a stable non-minimal state-space system

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In this paper we present a numerically reliable algorithm to compute the balanced realization of a stable state-space system that may be arbitrarily close to being unobservable and/or uncontrollable.…

A Novel Scheme for Positive Real Balanced Truncation

- Mathematics2007 American Control Conference
- 2007

A novel scheme for positive real balanced truncation of stable and passive systems will be proposed, which is a combination of the already existing Lyapunov balancing and Riccati balancing.