| 1. |
- Elmroth, Erik, 1964-, et al.
(författare)
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Orbit and Bundle Stratification for Controllability and Observability Matrix Pairs in StratiGraph
- 2004
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Ingår i: Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems (MTNS). ; , s. 1-9
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 2. |
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| 3. |
- Kågström, Bo, et al.
(författare)
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StratiGraph Tool : Matrix Stratifications in Control Applications
- 2012
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Ingår i: Control and Optimization with Differential-Algebraic Constraints. - Philadelphia : Society for Industrial and Applied Mathematics. - 9781611972245 ; , s. 79-103
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Bokkapitel (refereegranskat)abstract
- 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.
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| 4. |
- Kågström, Bo, et al.
(författare)
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StratiGraph Tool : Matrix Stratifications in Control Applications
- 2011
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 5. |
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| 6. |
- Elmroth, Erik, 1964-, et al.
(författare)
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A Web Computing Environment for the SLICOT Library
- 2001
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Ingår i: The Third NICONET Workshop on Numerical Control Software. ; , s. 53-61
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Tidskriftsartikel (refereegranskat)abstract
- A prototype web computing environment for computations related to the design and analysis of control systems using the SLICOT software library is presented. The web interface can be accessed from a standard world wide web browser with no need for additional software installations on the local machine. The environment provides user-friendly access to SLICOT routines where run-time options are specified by mouse clicks on appropriate buttons. Input data can be entered directly into the web interface by the user or uploaded from a local computer in a standard text format or in Matlab binary format. Output data is presented in the web browser window and possible to download in a number of different formats, including Matlab binary. The environment is ideal for testing the SLICOT software before performing a software installation or for performing a limited number of computations. It is also highly recommended for education as it is easy to use, and basically self-explanatory, with the users' guide integrated in the user interface.
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| 7. |
- Elmroth, Erik, 1964-, et al.
(författare)
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Bounds for the distance between nearby Jordan and Kronecker structures in a closure hierarchy
- 2003
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Ingår i: Journal of Mathematical Science. - 1072-3374. ; 114:6, s. 1765-1779
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 8. |
- Elmroth, Erik, 1964-, et al.
(författare)
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Computation and presentation of graphs displaying closure hierarchies of Jordan and Kronecker structures
- 2001
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Ingår i: Numerical Linear Algebra with Applications. - : John Wiley & Sons. - 1070-5325 .- 1099-1506. ; 8:6-7, s. 381-399
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Tidskriftsartikel (refereegranskat)abstract
- StratiGraph, a Java-based tool for computation and presentation of closure hierarchies of Jordan and Kronecker structures is presented. The tool is based on recent theoretical results on stratifications of orbits and bundles of matrices and matrix pencils. A stratification reveals the complete hierarchy of nearby structures. information critical for explaining the qualitative behaviour of linear systems under perturbations. StratiGraph facilitates the application of these theories and visualizes the resulting hierarchy as a graph. Nodes in the graph represent orbits or bundles of matrices or matrix pencils. Edges represent covering relations in the closure hierarchy. Given a Jordan or Kronecker structure, a user can obtain the complete information of nearby structures simply by mouse clicks on nodes of interest. This contribution gives an overview of the StratiGraph tool, presents its main functionalities and other features, and illustrates its use by sample applications. Copyright (C) 2001 John Wiley & Sons, Ltd.
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