11 research outputs found
Structured backward errors for eigenvalues of linear port-Hamiltonian descriptor systems
When computing the eigenstructure of matrix pencils associated with the
passivity analysis of perturbed port-Hamiltonian descriptor system using a
structured generalized eigenvalue method, one should make sure that the
computed spectrum satisfies the symmetries that corresponds to this structure
and the underlying physical system. We perform a backward error analysis and
show that for matrix pencils associated with port-Hamiltonian descriptor
systems and a given computed eigenstructure with the correct symmetry structure
there always exists a nearby port-Hamiltonian descriptor system with exactly
that eigenstructure. We also derive bounds for how near this system is and show
that the stability radius of the system plays a role in that bound
Random Perturbations of Matrix Polynomials
A sum of a large-dimensional random matrix polynomial and a fixed low-rank
matrix polynomial is considered. The main assumption is that the resolvent of
the random polynomial converges to some deterministic limit. A formula for the
limit of the resolvent of the sum is derived and the eigenvalues are localised.
Three instances are considered: a low-rank matrix perturbed by the Wigner
matrix, a product of a fixed diagonal matrix and the Wigner matrix
and a special matrix polynomial. The results are illustrated with various
examples and numerical simulations.Comment: 28 pages, 5 figure
Automated Generation of Explicit Port-Hamiltonian Models from Multi-Bond Graphs
Port-Hamiltonian system theory is a well-known framework for the control of complex physical systems. The majority of port-Hamiltonian control design methods base on an \emph{explicit} input-state-output port-Hamiltonian model for the system under consideration. However in the literature, little effort has been made towards a systematic, automatable derivation of such explicit models.
In this paper, we present a constructive, formally rigorous method for an explicit port-Hamiltonian formulation of multi-bond graphs. Two conditions, one necessary and one sufficient, for the existence of an explicit port-Hamiltonian formulation of a multi-bond graph are given. We summarise our approach in a fully automated algorithm of which we provide an exemplary implementation along with this publication. The theoretical and practical results are illustrated through an academic example