2012/08/17 by Marko Šešlija, Seslija, Marko, Jacquelien M.A. Scherpen +3
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · Mathematics · #Algebraic and Geometric Analysis #Control and Stability of Dynamical Systems #FOS: Electrical engineering #FOS: Mathematics #Microtubule and mitosis dynamics #Numerical methods for differential equations #Optimization and Control (math.OC) #Systems and Control (eess.SY) #Topological and Geometric Data Analysis #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1208.3549
openalex publication_date 2012/08/17 · openalex created_date 2022/08/13 · openalex updated_date 2026/07/28
Simplicial Dirac structures as finite analogues of the canonical Stokes-Dirac\nstructure, capturing the topological laws of the system, are defined on\nsimplicial manifolds in terms of primal and dual cochains related by the\ncoboundary operators. These finite-dimensional Dirac structures offer a\nframework for the formulation of standard input-output finite-dimensional\nport-Hamiltonian systems that emulate the behavior of distributed-parameter\nport-Hamiltonian systems. This paper elaborates on the matrix representations\nof simplicial Dirac structures and the resulting port-Hamiltonian systems on\nsimplicial manifolds. Employing these representations, we consider the\nexistence of structural invariants and demonstrate how they pertain to the\nenergy shaping of port-Hamiltonian systems on simplicial manifolds.\n