Linear port-Hamiltonian descriptor systems. (English) Zbl 1401.37070
Summary: The modeling framework of port-Hamiltonian systems is systematically extended to linear constrained dynamical systems (descriptor systems, differential-algebraic equations) of arbitrary index and with time-varying constraints. A new algebraically and geometrically defined system structure is derived. It is shown that this structure is invariant under equivalence transformations, and that it is adequate also for the modeling of high-index descriptor systems. The regularization procedure for descriptor systems to make them suitable for simulation and control is modified to preserve the port-Hamiltonian form. The relevance of the new structure is demonstrated with several examples.
MSC:
| 37K05 | Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010) |
| 65L80 | Numerical methods for differential-algebraic equations |
| 93B17 | Transformations |
| 93B11 | System structure simplification |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 93C05 | Linear systems in control theory |
Keywords:
port-Hamiltonian system; descriptor system; differential-algebraic equation; passivity; stability; system transformation; differentiation index; strangeness-index; skew-adjoint operatorSoftware:
SIMPACKReferences:
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