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Preprint 09-2017

Condensed Forms for linear Port-Hamiltonian Descriptor Systems

Source file is available as :   Portable Document Format (PDF)

Author(s) : Lena Scholz

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 09-2017

MSC 2000

34H05 Control problems
93A30 Mathematical modeling
93B11 System structure simplification
93B17 Transformations
93C05 Linear systems
93C15 Systems governed by ordinary differential equations

Abstract :
Motivated by the structure which arises in the port-Hamiltonian formulation of constraint dynamical systems, we derive structure preserving condensed forms for skew-adjoint differential-algebraic equations (DAEs). Moreover, structure preserving condensed forms under constant rank assumptions for linear port-Hamiltonian differential-algebraic equations are developed. These condensed forms allow us to further analyze the properties of port-Hamiltonian DAEs and to study e.g. existence and uniqueness of solutions. As examples the equations of motion of linear multibody systems and of linear electrical circuit equations are considered.

Keywords : Port-Hamiltonian system, descriptor system, differential-algebraic equation, system transformation, strangeness index, skew-adjoint pair of matrix functions, condensed form

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