Exponential stability of boundary controlled port Hamiltonian systems with dynamic feedback

Hector Ramirez; Hans Zwart; Yann Le Gorrec

doi:10.3182/20130925-3-FR-4043.00085

Exponential stability of boundary controlled port Hamiltonian systems with dynamic feedback

Hector Ramirez, Hans Zwart^*, Yann Le Gorrec

^*Corresponding author for this work

Research output: Contribution to journal › Conference article › Academic › peer-review

4 Citations (Scopus)

133 Downloads (Pure)

Abstract

In this paper it is shown that an input strictly passive linear finite dimensional port-Hamiltonian controller exponentially stabilizes a large class of boundary control systems. This follows since the finite dimensional controller dissipates the energy flowing through the boundaries of the infinite dimensional system. The assumptions on the controller is that it is input strictly passive and that it is exponentially stable. The result is illustrated on the model of a boundary controlled DNA-manipulation process.

Original language	English
Pages (from-to)	115-120
Number of pages	6
Journal	IFAC Proceedings Volumes (IFAC-PapersOnline)
Volume	46
Issue number	26
DOIs	https://doi.org/10.3182/20130925-3-FR-4043.00085
Publication status	Published - 1 Jan 2013
Event	1st IFAC Workshop on Control of Systems Governed by Partial Differential Equations, CPDE 2013 - Paris, France Duration: 25 Sept 2013 → 27 Sept 2013 Conference number: 1

Keywords

Boundary control systems
Exponential stability
Infinite dimensional port Hamiltonian systems
Passivity

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10.3182/20130925-3-FR-4043.00085

2013 Hector RamirezAccepted author version, 355 KB

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title = "Exponential stability of boundary controlled port Hamiltonian systems with dynamic feedback",

abstract = "In this paper it is shown that an input strictly passive linear finite dimensional port-Hamiltonian controller exponentially stabilizes a large class of boundary control systems. This follows since the finite dimensional controller dissipates the energy flowing through the boundaries of the infinite dimensional system. The assumptions on the controller is that it is input strictly passive and that it is exponentially stable. The result is illustrated on the model of a boundary controlled DNA-manipulation process.",

keywords = "Boundary control systems, Exponential stability, Infinite dimensional port Hamiltonian systems, Passivity",

author = "Hector Ramirez and Hans Zwart and {Le Gorrec}, Yann",

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T1 - Exponential stability of boundary controlled port Hamiltonian systems with dynamic feedback

AU - Ramirez, Hector

AU - Zwart, Hans

AU - Le Gorrec, Yann

N1 - Conference code: 1

PY - 2013/1/1

Y1 - 2013/1/1

N2 - In this paper it is shown that an input strictly passive linear finite dimensional port-Hamiltonian controller exponentially stabilizes a large class of boundary control systems. This follows since the finite dimensional controller dissipates the energy flowing through the boundaries of the infinite dimensional system. The assumptions on the controller is that it is input strictly passive and that it is exponentially stable. The result is illustrated on the model of a boundary controlled DNA-manipulation process.

AB - In this paper it is shown that an input strictly passive linear finite dimensional port-Hamiltonian controller exponentially stabilizes a large class of boundary control systems. This follows since the finite dimensional controller dissipates the energy flowing through the boundaries of the infinite dimensional system. The assumptions on the controller is that it is input strictly passive and that it is exponentially stable. The result is illustrated on the model of a boundary controlled DNA-manipulation process.

KW - Boundary control systems

KW - Exponential stability

KW - Infinite dimensional port Hamiltonian systems

KW - Passivity

U2 - 10.3182/20130925-3-FR-4043.00085

DO - 10.3182/20130925-3-FR-4043.00085

M3 - Conference article

AN - SCOPUS:84896534384

SN - 1474-6670

VL - 46

SP - 115

EP - 120

JO - IFAC Proceedings Volumes (IFAC-PapersOnline)

JF - IFAC Proceedings Volumes (IFAC-PapersOnline)

IS - 26

T2 - 1st IFAC Workshop on Control of Systems Governed by Partial Differential Equations, CPDE 2013

Y2 - 25 September 2013 through 27 September 2013

ER -

Exponential stability of boundary controlled port Hamiltonian systems with dynamic feedback

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Keywords

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