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Publications (10 of 13) Show all publications
Kågström, B., Johansson, S. & Johansson, P. (2012). StratiGraph Tool: Matrix Stratifications in Control Applications. In: Lorenz T. Biegler, Stephen L. Champbell, Volker Mehrmann (Ed.), Control and Optimization with Differential-Algebraic Constraints: (pp. 79-103). Philadelphia: Society for Industrial and Applied Mathematics
Open this publication in new window or tab >>StratiGraph Tool: Matrix Stratifications in Control Applications
2012 (English)In: Control and Optimization with Differential-Algebraic Constraints / [ed] Lorenz T. Biegler, Stephen L. Champbell, Volker Mehrmann, Philadelphia: Society for Industrial and Applied Mathematics, 2012, p. 79-103Chapter in book (Refereed)
Abstract [en]

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.

Place, publisher, year, edition, pages
Philadelphia: Society for Industrial and Applied Mathematics, 2012
Series
Advances in Design and Control ; 23
Keywords
Stratification, differential-algebraic equations, descriptor systems, Kronecker structures, orbit, bundle, closure hierarchy, cover relations, StratiGraph
National Category
Computational Mathematics Computer Sciences
Research subject
Numerical Analysis; Automatic Control
Identifiers
urn:nbn:se:umu:diva-61417 (URN)978-1-611972-24-5 (ISBN)
Funder
eSSENCE - An eScience CollaborationSwedish Foundation for Strategic Research , A3 02:128
Available from: 2012-11-13 Created: 2012-11-13 Last updated: 2019-06-26Bibliographically approved
Kågström, B., Johansson, S. & Johansson, P. (2011). StratiGraph Tool: Matrix Stratifications in Control Applications. Umeå: Department of Computing Science, Umeå University
Open this publication in new window or tab >>StratiGraph Tool: Matrix Stratifications in Control Applications
2011 (English)Report (Other academic)
Abstract [en]

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.

Place, publisher, year, edition, pages
Umeå: Department of Computing Science, Umeå University, 2011. p. 24
Series
Report / UMINF, ISSN 0348-0542 ; 11.12
Keywords
Stratification, differential-algebraic equations, descriptor systems, Kronecker structures, orbit, bundle, closure hierarchy, cover relations, StratiGraph
National Category
Computer Sciences Computational Mathematics
Research subject
Numerical Analysis; Automatic Control
Identifiers
urn:nbn:se:umu:diva-50774 (URN)
External cooperation:
Available from: 2012-01-02 Created: 2011-12-21 Last updated: 2019-06-26Bibliographically approved
Johansson, P. (2006). Matrix canonical structure toolbox. Umeå: Universitet, UMINF(15)
Open this publication in new window or tab >>Matrix canonical structure toolbox
2006 (English)Report (Other (popular science, discussion, etc.))
Place, publisher, year, edition, pages
Umeå: Universitet, 2006
Series
Report / UMINF, ISSN 0348-0542 ; 06:15
Keywords
Matlab, StratiGraph, Canonical Structures
National Category
Software Engineering
Identifiers
urn:nbn:se:umu:diva-5405 (URN)
Available from: 2006-10-11 Created: 2006-10-11 Last updated: 2019-06-26Bibliographically approved
Johansson, P. (2006). Software tools for matrix canonical computations and web-based software library environments. (Doctoral dissertation). Umeå: Datavetenskap
Open this publication in new window or tab >>Software tools for matrix canonical computations and web-based software library environments
2006 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This dissertation addresses the development and use of novel software tools and environments for the computation and visualization of canonical information as well as stratification hierarchies for matrices and matrix pencils.

The simplest standard shape to which a matrix pencil with a given set of eigenvalues can be reduced is called the Kronecker canonical form (KCF). The KCF of a matrix pencil is unique, and all pencils in the manifold of strictly equivalent pencils - collectively termed the orbit - can be reduced to the same canonical form and so have the same canonical structure. For a problem with fixed input size, all orbits are related under small perturbations. These relationships can be represented in a closure hierarchy with a corresponding graph depicting the stratification of these orbits. Since degenerate canonical structures are common in many applications, software tools to determine canonical information, especially under small perturbations, are central to understanding the behavior of these problems.

The focus in this dissertation is the development of a software tool called StratiGraph. Its purpose is the computation and visualization of stratification graphs of orbits and bundles (i.e., union of orbits in which the eigenvalues may change) for matrices and matrix pencils. It also supports matrix pairs, which are common in control systems. StratiGraph is extensible by design, and a well documented plug-in feature enables it, for example, to communicate with Matlab(TM). The use and associated benefits of StratiGraph are illustrated via numerous examples. Implementation considerations such as flexible software design, suitable data representations, and good and efficient graph layout algorithms are also discussed.

A way to estimate upper and lower bounds on the distance between an input S and other orbits is presented. The lower bounds are of Eckhart-Young type, based on the matrix representation of the associated tangent spaces. The upper bounds are computed as the Frobenius norm F of a perturbation such that S + F is in the manifold defining a specified orbit. Using associated plug-ins to StratiGraph this information can be computed in Matlab, while visualization alongside other canonical information remains within StratiGraph itself.

Also, a proposal of functionality and structure of a framework for computation of matrix canonical structure is presented. Robust, well-known algorithms, as well algorithms improved and developed in this work, are used. The framework is implemented as a prototype Matlab toolbox. The intention is to collect software for computing canonical structures as well as for computing bounds and to integrate it with the theory of stratification into a powerful new environment called the MCS toolbox.

Finally, a set of utilities for generating web computing environments related to mathematical and engineering library software is presented. The web interface can be accessed from a standard web browser with no need for additional software installation on the local machine. Integration with the control and systems library SLICOT further demonstrates the efficacy of this approach.

Place, publisher, year, edition, pages
Umeå: Datavetenskap, 2006. p. 30
Series
Report / UMINF, ISSN 0348-0542 ; 06.30
Keywords
Canonical structure, Jordan canonical form, controllability, StratiGraph, Matlab toolbox, Kronecker canonical form, matrix, matrix pencil, perturbation theory, closure hirerarchy, matrix stratification, control system, observability
National Category
Computational Mathematics
Identifiers
urn:nbn:se:umu:diva-890 (URN)91-7264-144-X (ISBN)
Public defence
2006-11-03, MA121, MIT, Umeå Universitet, Umeå, 13:15 (English)
Opponent
Supervisors
Available from: 2006-10-11 Created: 2006-10-11 Last updated: 2019-06-26Bibliographically approved
Johansson, P. (2006). StratiGraph developer's guide. Umeå: Umeå Universitet, UMINF(14)
Open this publication in new window or tab >>StratiGraph developer's guide
2006 (English)Report (Other academic)
Place, publisher, year, edition, pages
Umeå: Umeå Universitet, 2006
Series
Report / UMINF, ISSN 0348-0542 ; 06:14
Keywords
Canonical structures, StratiGraph, Sowftware development
National Category
Software Engineering
Research subject
computer and systems sciences
Identifiers
urn:nbn:se:umu:diva-5404 (URN)
Available from: 2006-10-11 Created: 2006-10-11 Last updated: 2019-06-26Bibliographically approved
Johansson, P. (2006). StratiGraph software design and algorithms. , UMINF-06.16
Open this publication in new window or tab >>StratiGraph software design and algorithms
2006 (English)Report (Other (popular science, discussion, etc.))
Series
Report / UMINF, ISSN 0348-0542 ; 06:16
Keywords
StratiGraph, Software Development
National Category
Software Engineering
Research subject
computer and systems sciences
Identifiers
urn:nbn:se:umu:diva-5402 (URN)
Available from: 2006-10-11 Created: 2006-10-11 Last updated: 2019-06-26Bibliographically approved
Elmroth, E., Johansson, P., Johansson, S. & Kågström, B. (2004). Orbit and Bundle Stratification for Controllability and Observability Matrix Pairs in StratiGraph. In: Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems (MTNS) (pp. 1-9).
Open this publication in new window or tab >>Orbit and Bundle Stratification for Controllability and Observability Matrix Pairs in StratiGraph
2004 (English)In: Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems (MTNS), 2004, p. 1-9Conference paper, Published paper (Refereed)
Abstract [en]

The canonical structures of controllability and observability pairs (A,B) and (A,C) associated with a state-space system are studied under small perturbations. We show how previous work for general matrix pencils can be applied to the stratification of orbits and bundles of matrix pairs. A stratification provides qualitative information about the closure relation between canonical structures.We also present how the new results are used in StratiGraph, which is a software tool for computing and visualizing closure hierarchies.

Identifiers
urn:nbn:se:umu:diva-9625 (URN)
Available from: 2008-05-05 Created: 2008-05-05 Last updated: 2019-06-26Bibliographically approved
Elmroth, E., Johansson, P., Johansson, S. & Kågström, B. (2004). Orbit and bundle stratification of controllability and observability matrix pairs in StratiGraph. Proceedings MTNS 2004
Open this publication in new window or tab >>Orbit and bundle stratification of controllability and observability matrix pairs in StratiGraph
2004 (English)In: Proceedings MTNS 2004Article in journal (Refereed) Published
Identifiers
urn:nbn:se:umu:diva-5401 (URN)
Available from: 2006-10-11 Created: 2006-10-11 Last updated: 2019-06-26
Elmroth, E., Johansson, P. & Kågström, B. (2003). Bounds for the distance between nearby Jordan and Kronecker structures in a closure hierarchy. Journal of Mathematical Science, 114(6), 1765-1779
Open this publication in new window or tab >>Bounds for the distance between nearby Jordan and Kronecker structures in a closure hierarchy
2003 (English)In: Journal of Mathematical Science, ISSN 1072-3374, Vol. 114, no 6, p. 1765-1779Article in journal (Refereed) Published
Abstract [en]

Computing the fine-canonical-structure elements of matrices and matrix pencils are ill-posed problems. Therefore, besides knowing the canonical structure of a matrix or a matrix pencil, it is equally important to know what are the nearby canonical structures that explain the behavior under small perturbations. Qualitative strata information is provided by our StratiGraph tool. Here, we present lower and upper bounds for the distance between Jordan and Kronecker structures in a closure hierarchy of an orbit or bundle stratification. This quantitative information is of importance in applications, e.g., distance to more degenerate systems (uncontrollability). Our upper bounds are based on staircase regularizing perturbations. The lower bounds are of EckartYoung type and are derived from a matrix representation of the tangent space of the orbit of a matrix or a matrix pencil. Computational results illustrate the use of the bounds.

Identifiers
urn:nbn:se:umu:diva-5400 (URN)
Available from: 2006-10-11 Created: 2006-10-11 Last updated: 2019-06-26
Johansson, P. (2003). StratiGraph user's guide. Umeå: University, UMINF(21)
Open this publication in new window or tab >>StratiGraph user's guide
2003 (English)Report (Other academic)
Place, publisher, year, edition, pages
Umeå: University, 2003
Series
Phonum : reports in phonetics, ISSN 1101-2714 ; 03:23
Keywords
StratiGraph, Software Developement
National Category
Software Engineering
Research subject
computer and systems sciences
Identifiers
urn:nbn:se:umu:diva-5403 (URN)
Available from: 2006-10-11 Created: 2006-10-11 Last updated: 2019-06-26Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-9957-7728

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