Correction to: Relative genericity of controllability and stabilizability for differential-algebraic systems

Ilchmann, Achim; Kirchhoff, Jonas

doi:10.1007/s00498-023-00355-4

Cited by 2 publications

(4 citation statements)

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“…We have derived criteria for (relative) genericity of observability for linear timeinvariant differential-algebraic systems and in particular for port-Hamiltonian descriptor systems. This extends on the one hand the well-known genericity of observability of linear time-invariant ordinary differential equations [15] to DAEs, and on the other hand the (relative) genericity of controllability of unstructured [5][6][7] and port-Hamiltonian DAEs [8] to observability.…”

Section: Discussionsupporting

confidence: 53%

Generic observability for port-Hamiltonian descriptor systems

Kirchhoff

2024

Math. Control Signals Syst.

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The present work is a successor of Ilchmann and Kirchhoff (Math Control Signals Syst 33:359–377, 2021. https://doi.org/10.1007/s00498-021-00287-x), Ilchmann and Kirchhoff (Math Control Signals Syst 35:45–76, 2023. https://doi.org/10.1007/s00498-021-00287-x) on (relative) generic controllability of unstructured linear differential-algebraic systems and of Ilchmann et al. (Port-Hamiltonian descriptor systems are generically controllable and stabilizable. Submitted to Mathematics of Control, Signals and Systems, 2023. https://arxiv.org/abs/2302.05156) on (relative) generic controllability of port-Hamiltonian descriptor systems. We extend their results to (relative) genericity of observability. For unstructured differential-algebraic systems, criteria for (relative) generic observability are derived from Ilchmann and Kirchhoff (Math Control Signals Syst 35:45–76, 2023. https://doi.org/10.1007/s00498-021-00287-x) using duality. This is not possible for port-Hamiltonian systems. Hence, we tweak the results of Ilchmann et al. (Port-Hamiltonian descriptor systems are generically controllable and stabilizable. Submitted to Mathematics of Control, Signals and Systems, 2023. https://arxiv.org/abs/2302.05156) and derive similar criteria as for the unstructured case. Additionally, we consider certain rank constraints on the system matrices.

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Section: Discussionsupporting

confidence: 53%

Generic observability for port-Hamiltonian descriptor systems

Kirchhoff

2024

Math. Control Signals Syst.

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“…The definition of "relative genericity" and other notions can be found in [1]. Before proving Proposition 2, we show that Step (iv).4 in the proof of [1, Prop.…”

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confidence: 92%

“…

The reasoning in Step (iv).4 in the proof of [1, Prop. 2.6] is erroneous: In line 4 of the step, we say "The induction assumption implies that …"; however, this does notInstead of fixing the error and proving (1) directly, we show Proposition 2 which is the ever so slightly more general result encompassing (1) and which might be worth knowing in its own right.For the formulation of our result, we need to define some matrix actions and some sets related to the Gaussian algorithm of elementary row operations.

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confidence: 98%