On the stability of port-Hamiltonian descriptor systems

Gernandt, Hannes; Haller, Frédéric Enrico

doi:10.1016/j.ifacol.2021.11.068

Cited by 7 publications

(8 citation statements)

References 11 publications

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“…(vii) [20] consider stable systems, i.e. for all consistent initial values x 0 ∈ K n the solution x to E ẋ(t) = Ax(t), x(0) = x 0 fulfills sup t≥0 x(t) < ∞.…”

Section: Literature Review and Combination Of Known Resultsmentioning

confidence: 99%

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The difference between port-Hamiltonian, passive and positive real descriptor systems

Cherifi¹,

Gernandt²,

Hinsen³

2022

Preprint

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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 descriptor systems. It is well-known that port-Hamiltonian systems are passive and that passive systems are positive real. Hence it is studied under which assumptions the converse implications hold. Furthermore, the relationship between passivity, KYP inequalities and a finite available storage is investigated.

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“…(vii) [20] consider stable systems, i.e. for all consistent initial values x 0 ∈ K n the solution x to E ẋ(t) = Ax(t), x(0) = x 0 fulfills sup t≥0 x(t) < ∞.…”

Section: Literature Review and Combination Of Known Resultsmentioning

confidence: 99%

“…Assume that Cz = 0. Then all α > 0 sufficiently small would violate (20). This contradiction leads to z ∈ ker C which implies ker Q ⊆ ker C. Hence Proposition 7.2 in [8] implies ker Q = {0}.…”

Section: When Does (Kyp) Imply (Ph)?mentioning

confidence: 96%

The difference between port-Hamiltonian, passive and positive real descriptor systems

Cherifi¹,

Gernandt²,

Hinsen³

2022

Preprint

Self Cite

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“…The pH formulation for continuous-time descriptor systems also allows for semidefinite Hamiltonians H. However, this may lead to pH descriptor systems which are unstable without imposing further assumptions, see [39,23]. The same is true for discrete-time systems, which is why we restrict ourselves to positive definite matrices X (X ) in Definition 4.1.…”

Section: Port-hamiltonian Representation Of Discrete-time Dissipative...mentioning

confidence: 99%

On discrete-time port-Hamiltonian (descriptor) systems

Cherifi¹,

Gernandt²,

Hinsen³

et al. 2023

Preprint

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Port-Hamiltonian (pH) systems have been studied extensively for linear continuous-time dynamical systems. In this manuscript a discrete-time pH descriptor formulation is presented for linear, completely causal, scattering passive dynamical systems that is purely based on the system coefficients. The relation of this formulation to positive and bounded real systems and the characterization via positive semidefinite solutions of Kalman-Yakubovich-Popv inequalities is also studied.

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“…For LTI DAE systems the characterization of stability via different generalized Lyapunov equations and the relation to pHDAE systems has recently been studied in different contexts e.g. in a behavior context in [85], via generalized Kalman-Yakubovich-Popov inequalities in [190,193], or via linear relations in [86].…”

Section: Remark 723 It Has Been Shown Inmentioning

confidence: 99%

Control of port-Hamiltonian differential-algebraic systems and applications

Mehrmann¹,

Unger²

2022

Preprint

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The modeling framework of port-Hamiltonian descriptor systems and their use in numerical simulation and control are discussed. The structure is ideal for automated network-based modeling since it is invariant under power-conserving interconnection, congruence transformations, and Galerkin projection. Moreover, stability and passivity properties are easily shown. Condensed forms under orthogonal transformations present easy analysis tools for existence, uniqueness, regularity, and numerical methods to check these properties.After recalling the concepts for general linear and nonlinear descriptor systems, we demonstrate that many difficulties that arise in general descriptor systems can be easily overcome within the port-Hamiltonian framework. The properties of port-Hamiltonian descriptor systems are analyzed, time-discretization, and numerical linear algebra techniques are discussed. Structure-preserving regularization procedures for descriptor systems are presented to make them suitable for simulation and control. Model reduction techniques that preserve the structure and stabilization and optimal control techniques are discussed.The properties of port-Hamiltonian descriptor systems and their use in modeling simulation and control methods are illustrated with several examples from different physical domains. The survey concludes with open problems and research topics that deserve further attention.

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On the stability of port-Hamiltonian descriptor systems

Cited by 7 publications

References 11 publications

The difference between port-Hamiltonian, passive and positive real descriptor systems

The difference between port-Hamiltonian, passive and positive real descriptor systems

On discrete-time port-Hamiltonian (descriptor) systems

Control of port-Hamiltonian differential-algebraic systems and applications

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