Umeå universitets logga

Incoherent scatter radar (ISR) techniques provide reliable measurements for the analysis of ionospheric plasma. Recent developments in ISR technologies allow the generation of high-resolution 3D data. Examples of such technologies employ the so-called phased-array antenna systems like the AMISR systems in North America or the upcoming EISCAT_3D in the Northern Fennoscandia region. EISCAT_3D will be capable of generating the highest resolution ISR datasets that have ever been measured. We present a novel fast computational strategy for the generation of high-resolution and smooth volumetric ionospheric images that represent ISR data. Through real-time processing, our computational framework will enable a fast decision-making during the monitoring process, where the experimental parameters are adapted in real time as the radars monitor specific phenomena. Real-time monitoring would allow the radar beams to be conveniently pointed at regions of interest and would therefore increase the science impact. We describe our strategy, which implements a flexible mesh generator along with an efficient interpolator specialized for ISR technologies. The proposed strategy is generic in the sense that it can be applied to a large variety of data sets and supports interactive visual analysis and exploration of ionospheric data, supplemented by interactive data transformations and filters.

We study how small perturbations of general matrix polynomials may change their elementary divisors and minimal indices by constructing the closure hierarchy (stratification) graphs of matrix polynomials' orbits and bundles. To solve this problem, we construct the stratification graphs for the first companion Fiedler linearization of matrix polynomials. Recall that the first companion Fiedler linearization as well as all the Fiedler linearizations is matrix pencils with particular block structures. Moreover, we show that the stratification graphs do not depend on the choice of Fiedler linearization which means that all the spaces of the matrix polynomial Fiedler linearizations have the same geometry (topology). This geometry coincides with the geometry of the space of matrix polynomials. The novel results are illustrated by examples using the software tool StratiGraph extended with associated new functionality.

We investigate the changes of the canonical structure information under small perturbations for a system pencil associated with a (generalized) linear time-invariant state-space system. The equivalence class of the pencil is taken with respect to feedback-injection equivalence transformations. The results allow us to track possible changes of important linear system characteristics under small perturbations.

We investigate the changes under small perturbations of the canonical structure information for a system pencil (A B C D) − s (E 0 0 0), det(E) ≠ 0, associated with a (generalized) linear time-invariant state-space system. The equivalence class of the pencil is taken with respect to feedback-injection equivalence transformation. The results allow to track possible changes under small perturbations of important linear system characteristics.

We study how small perturbations of matrix polynomials may change their elementary divisors and minimal indices by constructing the closure hierarchy graphs (stratifications) of orbits and bundles of matrix polynomial Fiedler linearizations. We show that the stratifica-tion graphs do not depend on the choice of Fiedler linearization which means that all the spaces of the matrix polynomial Fiedler lineariza-tions have the same geometry (topology). The results are illustrated by examples using the software tool StratiGraph.

Matlab functions to work with the canonical structures for congru-ence and *congruence of matrices, and for congruence of symmetricand skew-symmetric matrix pencils are presented. A user can providethe canonical structure objects or create (random) matrix examplesetups with a desired canonical information, and compute the codi-mensions of the corresponding orbits: if the structural information(the canonical form) of a matrix or a matrix pencil is known it isused for the codimension computations, otherwise they are computednumerically. Some auxiliary functions are provided too. All thesefunctions extend the Matrix Canonical Structure Toolbox.

We show that perturbations of polynomial matrices of full normal-rank can be analyzed viathe study of perturbations of companion form linearizations of such polynomial matrices.It is proved that a full normal-rank polynomial matrix has the same structural elements asits right (or left) linearization. Furthermore, the linearized pencil has a special structurethat can be taken into account when studying its stratification. This yields constraintson the set of achievable eigenstructures. We explicitly show which these constraints are.These results allow us to derive necessary and sufficient conditions for cover relationsbetween two orbits or bundles of the linearization of full normal-rank polynomial matrices.The stratification rules are applied to and illustrated on two artificial polynomial matricesand a half-car passive suspension system with four degrees of freedom.

In this contribution, the software tool StratiGraph for computing and visualizing closurehierarchy graphs associated with different orbit and bundle stratifications is presented. Inaddition, we review the underlying theory and illustrate how StratiGraph can be used toanalyze descriptor system models via their associated system pencils. The stratificationtheory provides information for a deeper understanding of how the dynamics of a controlsystem and its system characteristics behave under perturbations.

In this contribution, the software tool StratiGraph for computing and visualizing closure hierarchy graphs associated with different orbit and bundle stratifications is presented. In addition, we review the underlying theory and illustrate how StratiGraph can be used to analyze descriptor system models via their associated system pencils. The stratification theory provides information for a deeper understanding of how the dynamics of a control system and its system characteristics behave under perturbations.

Efficient and accurate structure exploiting numerical methods for solvingthe periodic Riccati differential equation (PRDE) are addressed. Such methods areessential, for example, to design periodic feedback controllers for periodic controlsystems. Three recently proposed methods for solving the PRDE are presented andevaluated on challenging periodic linear artificial systems with known solutions and applied to the stabilization of periodic motions of mechanical systems. The first twomethods are of the type multiple shooting and rely on computing the stable invariantsubspace of an associated Hamiltonian system. The stable subspace is determinedusing either algorithms for computing an ordered periodic real Schur form of a cyclicmatrix sequence, or a recently proposed method which implicitly constructs a stabledeflating subspace from an associated lifted pencil. The third method reformulatesthe PRDE as a convex optimization problem where the stabilizing solution is approximatedby its truncated Fourier series. As known, this reformulation leads to a semidefiniteprogramming problem with linear matrix inequality constraints admitting aneffective numerical realization. The numerical evaluation of the PRDE methods, withfocus on the number of states (n) and the length of the period (T ) of the periodicsystems considered, includes both quantitative and qualitative results.