On the equivalence of geometric and descriptor representations of linear port-Hamiltonian systems

2023/05/14 by Hannes Gernandt, Gernandt, Hannes, Friedrich Philipp +5
Engineering · Mathematics · Computer Science · #Control and Stability of Dynamical Systems #Numerical methods for differential equations #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2305.08270

Abstract

We prove a one-to-one correspondence between the geometric formulation of port-Hamiltonian (pH) systems defined by Dirac structures, Lagrange structures, maximal resistive structures, and external ports and a state-space formulation by means of port-Hamiltonian descriptor systems, i.e., differential algebraic equations (DAE) with inputs and outputs.

Related

• Port-Hamiltonian descriptor systems
• Linear port-Hamiltonian DAE systems revisited
• Control of port-Hamiltonian differential-algebraic systems and applications
• A linear relation approach to port-Hamiltonian differential-algebraic equations
• Structure-preserving discretization for port-Hamiltonian descriptor\n systems