Differential–algebraic systems with dissipative Hamiltonian structure
Volker Mehrmann, Arjan van der Schaft
Abstract
Abstract Different representations of linear dissipative Hamiltonian and port-Hamiltonian differential–algebraic equations (DAE) systems are presented and compared. Using global geometric and algebraic points of view, translations between different representations are presented. Characterizations are also derived when a general DAE system can be transformed into one of these structured representations. Approaches for computing the structural information and the described transformations are derived that can be directly implemented as numerical methods. The results are demonstrated with a large number of examples.
Topics & Concepts
Dissipative systemAlgebraic numberDifferential algebraic geometryHamiltonian systemMathematicsAlgebra over a fieldHamiltonian (control theory)Real algebraic geometryAlgebraic structureDifferential equationOrdinary differential equationPure mathematicsDifferential algebraic equationMathematical analysisPhysicsMathematical optimizationQuantum mechanicsControl and Stability of Dynamical SystemsNumerical methods for differential equationsModeling and Simulation Systems