23,945 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
On computing minimal realizations of periodic descriptor systems
Abstract: We propose computationally efficient and numerically reliable algorithms to compute minimal realizations of periodic descriptor systems. The main computational tool employed for the structural analysis of periodic descriptor systems (i.e., reachability and observability) is the orthogonal reduction of periodic matrix pairs to Kronecker-like forms. Specializations of a general reduction algortithm are employed for particular type of systems. One of the proposed minimal realization transformations for which the backward numerical stability can be proved
Model Reduction of Descriptor Systems by Interpolatory Projection Methods
In this paper, we investigate interpolatory projection framework for model
reduction of descriptor systems. With a simple numerical example, we first
illustrate that employing subspace conditions from the standard state space
settings to descriptor systems generically leads to unbounded H2 or H-infinity
errors due to the mismatch of the polynomial parts of the full and
reduced-order transfer functions. We then develop modified interpolatory
subspace conditions based on the deflating subspaces that guarantee a bounded
error. For the special cases of index-1 and index-2 descriptor systems, we also
show how to avoid computing these deflating subspaces explicitly while still
enforcing interpolation. The question of how to choose interpolation points
optimally naturally arises as in the standard state space setting. We answer
this question in the framework of the H2-norm by extending the Iterative
Rational Krylov Algorithm (IRKA) to descriptor systems. Several numerical
examples are used to illustrate the theoretical discussion.Comment: 22 page
Bounded real lemmas for positive descriptor systems
A well known result in the theory of linear positive systems is the existence of positive definite diagonal matrix (PDDM) solutions to some well known linear matrix inequalities (LMIs). In this paper, based on the positivity characterization, a novel bounded real lemma for continuous positive descriptor systems in terms of strict LMI is first established by the separating hyperplane theorem. The result developed here provides a necessary and sufficient condition for systems to possess H?H? norm less than ? and shows the existence of PDDM solution. Moreover, under certain condition, a simple model reduction method is introduced, which can preserve positivity, stability and H?H? norm of the original systems. An advantage of such method is that systems? matrices of the reduced order systems do not involve solving of LMIs conditions. Then, the obtained results are extended to discrete case. Finally, a numerical example is given to illustrate the effectiveness of the obtained results
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