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}
}

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References

SHOWING 1-10 OF 52 REFERENCES
Structure preserving reduction of port hamiltonian system using a modified LQG method
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
TLDR
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
TLDR
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.
Robust port-Hamiltonian representations of passive systems
Passivity and Structure Preserving Order Reduction of Linear Port-Hamiltonian Systems Using Krylov Subspaces
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
TLDR
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...
Truncated balanced realization of a stable non-minimal state-space system
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
TLDR
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.
...
...