The Experts below are selected from a list of 312 Experts worldwide ranked by ideXlab platform
Bo Kagstrom - One of the best experts on this subject based on the ideXlab platform.
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blocked algorithms for the reduction to hessenberg Triangular Form revisited
Bit Numerical Mathematics, 2008Co-Authors: Bo Kagstrom, Daniel Kressner, Enrique S Quintanaorti, Gregorio QuintanaortiAbstract:We present two variants of Moler and Stewart’s algorithm for reducing a matrix pair to Hessenberg-Triangular (HT) Form with increased data locality in the access to the matrices. In one of these variants, a careful reorganization and accumulation of Givens rotations enables the use of efficient level 3 BLAS. Experimental results on four different architectures, representative of current high perFormance processors, compare the perFormances of the new variants with those of the implementation of Moler and Stewart’s algorithm in subroutine DGGHRD from LAPACK, Dackland and Kagstrom’s two-stage algorithm for the HT Form, and a modified version of the latter which requires considerably less flops.
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PARA - Parallel Two-Stage Reduction of a Regular Matrix Pair to Hessenberg-Triangular Form
Applied Parallel Computing. New Paradigms for HPC in Industry and Academia, 2001Co-Authors: Bjorn Adlerborn, Krister Dackland, Bo KagstromAbstract:A parallel two-stage algorithm for reduction of a regular matrix pair (A,B) to Hessenberg-Triangular Form (H, T) is presented. Stage one reduces the matrix pair to a block upper Hessenberg-Triangular Form (Hr, T), where Hr is upper r-Hessenberg with r > 1 subdiagonals and T is upper Triangular. In stage two, the desired upper Hessenberg-Triangular Form is computed using two-sided Givens rotations. PerFormance results for the ScaLAPACK-style implementations show that the parallel algorithms can be used to solve large scale problems effectively.
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parallel two stage reduction of a regular matrix pair to hessenberg Triangular Form
Parallel Computing, 2000Co-Authors: Bjorn Adlerborn, Krister Dackland, Bo KagstromAbstract:A parallel two-stage algorithm for reduction of a regular matrix pair (A,B) to Hessenberg-Triangular Form (H, T) is presented. Stage one reduces the matrix pair to a block upper Hessenberg-Triangular Form (Hr, T), where Hr is upper r-Hessenberg with r > 1 subdiagonals and T is upper Triangular. In stage two, the desired upper Hessenberg-Triangular Form is computed using two-sided Givens rotations. PerFormance results for the ScaLAPACK-style implementations show that the parallel algorithms can be used to solve large scale problems effectively.
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a scalapack style algorithm for reducing a regular matrix pair to block hessenberg Triangular Form
Parallel Computing, 1998Co-Authors: Krister Dackland, Bo KagstromAbstract:A parallel algorithm for reduction of a regular matrix pair (A, B) to block Hessenberg-Triangular Form is presented. It is shown how a sequential elementwise algorithm can be reorganized in terms of blocked factorizations and matrix-matrix operations. Moreover, this LAPACK-style algorithm is straightforwardly extended to a parallel algorithm for a rectangular 2D processor grid using parallel kernels from ScaLAPACK. A hierarchical perFormance model is derived and used for algorithm analysis and selection of optimal blocking parameters and grid sizes.
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PARA - A ScaLAPACK-Style Algorithm for Reducing a Regular Matrix Pair to Block Hessenberg-Triangular Form
Lecture Notes in Computer Science, 1998Co-Authors: Krister Dackland, Bo KagstromAbstract:A parallel algorithm for reduction of a regular matrix pair (A, B) to block Hessenberg-Triangular Form is presented. It is shown how a sequential elementwise algorithm can be reorganized in terms of blocked factorizations and matrix-matrix operations. Moreover, this LAPACK-style algorithm is straightforwardly extended to a parallel algorithm for a rectangular 2D processor grid using parallel kernels from ScaLAPACK. A hierarchical perFormance model is derived and used for algorithm analysis and selection of optimal blocking parameters and grid sizes.
Markus Schoberl - One of the best experts on this subject based on the ideXlab platform.
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A structurally flat Triangular Form based on the extended chained Form
International Journal of Control, 2020Co-Authors: Conrad Gstottner, Bernd Kolar, Markus SchoberlAbstract:In this paper, we present a structurally flat Triangular Form which is based on the extended chained Form. We provide a complete geometric characterisation of the proposed Triangular Form in terms ...
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a structurally flat Triangular Form based on the extended chained Form
arXiv: Dynamical Systems, 2020Co-Authors: Conrad Gstottner, Bernd Kolar, Markus SchoberlAbstract:In this paper, we present a structurally flat Triangular Form which is based on the extended chained Form. We provide a complete geometric characterization of the proposed Triangular Form in terms of necessary and sufficient conditions for an affine input system with two inputs to be static feedback equivalent to this Triangular Form. This yields a sufficient condition for an affine input system to be flat.
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On a Flat Triangular Form Based on the Extended Chained Form
arXiv: Dynamical Systems, 2020Co-Authors: Conrad Gstottner, Bernd Kolar, Markus SchoberlAbstract:In this paper, we present a structurally flat Triangular Form which is based on the extended chained Form. We provide necessary and sufficient conditions for an affine input system with two inputs to be static feedback equivalent to the proposed Triangular Form, and thus a sufficient condition for an affine input system to be flat.
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Remarks on a Triangular Form for 1-Flat Pfaffian Systems with Two Inputs
IFAC-PapersOnLine, 2015Co-Authors: Bernd Kolar, Markus Schoberl, Kurt SchlacherAbstract:Abstract We consider 1-flat nonlinear control systems with two inputs and a given 1-flat output. The control systems are represented as Pfaffian systems. It is well-known that flat systems can be transFormed to Brunovsky normal Form after applying an endogenous dynamic feedback, and only for static feedback linearizable systems this transFormation is possible without dynamic feedback. However, there exists a normal Form, denoted as implicit Triangular Form, which is a generalization of the Brunovsky normal Form, and even systems which are not static feedback linearizable might possibly be transFormed to this normal Form without applying a dynamic feedback. Given a two-input nonlinear control system and a fixed 1-flat output, we provide necessary and suficient conditions to check whether such a transFormation exists. Furthermore, we provide an algorithm to find this transFormation.
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on an implicit Triangular decomposition of nonlinear control systems that are 1 flat a constructive approach
Automatica, 2014Co-Authors: Markus Schoberl, Kurt SchlacherAbstract:Abstract In this paper we investigate a Triangular Form based on implicit differential equations for nonlinear multi-input systems with respect to the flatness property. Furthermore, we suggest a constructive method for the transFormation of a given system into that special Triangular shape, if possible. The well-known Brunovsky Form, which is applicable with regard to the exact linearization problem, can be seen as a special case of this implicit Triangular Form. A key tool in our investigation will be the construction of Cauchy characteristic vector fields that additionally annihilate certain codistributions. In adapted coordinates this construction allows us to single out variables whose time-evolution can be derived without any integration.
Salim Ibrir - One of the best experts on this subject based on the ideXlab platform.
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Brief paper: Adaptive observers for time-delay nonlinear systems in Triangular Form
Automatica, 2009Co-Authors: Salim IbrirAbstract:A simple nonlinear observer with a dynamic gain is proposed for a class of bounded-state nonlinear systems subject to state delay. By saturating the states of the observer nonlinearities with either symmetric or non-symmetric saturation functions, we show that the observer exists, whatever the delay is. Furthermore, it will be highlighted that the observer design is free from any preliminary analysis of the time-delay system such as estimating the Lipschitz constants of nonlinearities. The proposed design encompasses a wide class of nonlinear and time-delay systems written in Triangular Form and generalizes previous results on delayless nonlinear systems.
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Observer-Based Control of Nonlinear Time-Delay Systems in Lower-Triangular Form
ASME 2009 Dynamic Systems and Control Conference Volume 2, 2009Co-Authors: Salim IbrirAbstract:Time-delay systems is a special class of dynamical systems that are frequently present in many fields of engineering. It has been shown in the literature that the existence of a stabilizing observer-based controller is related to delay-dependent conditions that are generally satisfied for a small time delay. Motivating works towards reducing the conservatism of the results are among the on-going research topics especially when partial-state measurements are imposed. This paper investigates the problem of observer-based stabilization of a class of time-delay nonlinear systems written in Triangular Form. First, we show that a delay nonlinear observer is globally convergent under the global Lipschitz condition of the system nonlinearity. Then, it is shown that a parameterized linear feedback that uses the observer states can stabilize the system whatever the size of the delay. Illustrative example is provided to approve the theoretical results.Copyright © 2009 by ASME
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ACC - Adaptive observer design for a class of nonlinear time-delay systems in lower-Triangular Form
2009 American Control Conference, 2009Co-Authors: Salim IbrirAbstract:A simple nonlinear observer with a dynamic gain is proposed for a class of bounded-state nonlinear systems subject to state delay. By saturating the states of the system nonlinearities, we show that the observer exists whatever the delay is. Furthermore, it will be highlighted that the observer design is free from any preliminary analysis of the time-delay system such as estimating the Lipschitz constants of nonlinearities. The proposed design encompasses a wide class of nonlinear and time-delay systems written in Triangular Form and generalizes previous results on delayless nonlinear systems.
Xianfu Zhang - One of the best experts on this subject based on the ideXlab platform.
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Feedback stabilisation control design for fractional order non-linear systems in the lower Triangular Form
IET Control Theory & Applications, 2016Co-Authors: Yige Zhao, Yuzhen Wang, Xianfu ZhangAbstract:Using the Lyapunov function method, this study investigates both state and output feedback stabilisation control design problems for fractional order non-linear systems in the lower Triangular Form, and presents a number of new results. First, some new properties for Caputo fractional derivative are presented. Second, by introducing appropriate transFormations of coordinates, the feedback stabiliser design problem is converted into the determination of finding some parameters, which can be obtained by solving the Lyapunov equation and relevant matrix inequalities. Finally, based on the Lyapunov function method, both state and output feedback stabilisers are explicitly designed to make the closed-loop system asymptotically stable. The study of an illustrative example shows that the obtained results are effective in designing feedback stabilisers for fractional order non-linear systems in the lower Triangular Form.
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asymptotical stabilization of fractional order linear systems in Triangular Form
Automatica, 2013Co-Authors: Lu Liu, Xianfu Zhang, Gang Feng, Yuzhen WangAbstract:In this paper, both state and output feedback stabilization controllers are designed for Triangular fractional-order linear time-invariant (FO-LTI) systems with fractional-order 0<@a<2. By introducing appropriate transFormations of coordinates, the problems of control design are converted into the problems of finding some parameters, which can be certainly obtained by solving relevant matrix inequalities. Contrary to many existing linear matrix inequalities (LMIs)-based approaches, all the matrix inequalities involved for the systems under study always have feasible solutions. A simulation example is given to demonstrate the effectiveness of the proposed controllers.
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Output feedback control of large-scale nonlinear time-delay systems in lower Triangular Form
Automatica, 2013Co-Authors: Xianfu Zhang, Lu Liu, Gang Feng, Chenghui ZhangAbstract:This paper is concerned with the stabilization problem for a class of large-scale nonlinear time-delay systems in lower Triangular Form. The uncertain nonlinearities are assumed to be bounded by continuous functions of the outputs or delayed outputs multiplied by unmeasured states or delayed states. An observer based output feedback control scheme is proposed using the dynamic gain control design approach. Based on Lyapunov stability theory, global asymptotic stability of the closed-loop control system is proved. Contrary to many existing control designs for lower Triangular nonlinear systems, the celebrated backstepping method is not utilized here. An example is finally given to demonstrate the effectiveness of the proposed design procedure.
Krister Dackland - One of the best experts on this subject based on the ideXlab platform.
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PARA - Parallel Two-Stage Reduction of a Regular Matrix Pair to Hessenberg-Triangular Form
Applied Parallel Computing. New Paradigms for HPC in Industry and Academia, 2001Co-Authors: Bjorn Adlerborn, Krister Dackland, Bo KagstromAbstract:A parallel two-stage algorithm for reduction of a regular matrix pair (A,B) to Hessenberg-Triangular Form (H, T) is presented. Stage one reduces the matrix pair to a block upper Hessenberg-Triangular Form (Hr, T), where Hr is upper r-Hessenberg with r > 1 subdiagonals and T is upper Triangular. In stage two, the desired upper Hessenberg-Triangular Form is computed using two-sided Givens rotations. PerFormance results for the ScaLAPACK-style implementations show that the parallel algorithms can be used to solve large scale problems effectively.
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parallel two stage reduction of a regular matrix pair to hessenberg Triangular Form
Parallel Computing, 2000Co-Authors: Bjorn Adlerborn, Krister Dackland, Bo KagstromAbstract:A parallel two-stage algorithm for reduction of a regular matrix pair (A,B) to Hessenberg-Triangular Form (H, T) is presented. Stage one reduces the matrix pair to a block upper Hessenberg-Triangular Form (Hr, T), where Hr is upper r-Hessenberg with r > 1 subdiagonals and T is upper Triangular. In stage two, the desired upper Hessenberg-Triangular Form is computed using two-sided Givens rotations. PerFormance results for the ScaLAPACK-style implementations show that the parallel algorithms can be used to solve large scale problems effectively.
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a scalapack style algorithm for reducing a regular matrix pair to block hessenberg Triangular Form
Parallel Computing, 1998Co-Authors: Krister Dackland, Bo KagstromAbstract:A parallel algorithm for reduction of a regular matrix pair (A, B) to block Hessenberg-Triangular Form is presented. It is shown how a sequential elementwise algorithm can be reorganized in terms of blocked factorizations and matrix-matrix operations. Moreover, this LAPACK-style algorithm is straightforwardly extended to a parallel algorithm for a rectangular 2D processor grid using parallel kernels from ScaLAPACK. A hierarchical perFormance model is derived and used for algorithm analysis and selection of optimal blocking parameters and grid sizes.
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PARA - A ScaLAPACK-Style Algorithm for Reducing a Regular Matrix Pair to Block Hessenberg-Triangular Form
Lecture Notes in Computer Science, 1998Co-Authors: Krister Dackland, Bo KagstromAbstract:A parallel algorithm for reduction of a regular matrix pair (A, B) to block Hessenberg-Triangular Form is presented. It is shown how a sequential elementwise algorithm can be reorganized in terms of blocked factorizations and matrix-matrix operations. Moreover, this LAPACK-style algorithm is straightforwardly extended to a parallel algorithm for a rectangular 2D processor grid using parallel kernels from ScaLAPACK. A hierarchical perFormance model is derived and used for algorithm analysis and selection of optimal blocking parameters and grid sizes.
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PARA - Reduction of a Regular Matrix Pair (A, B) to Block Hessenberg Triangular Form
Lecture Notes in Computer Science, 1996Co-Authors: Krister Dackland, Bo KagstromAbstract:An algorithm for reduction of a regular matrix pair (A, B) to block Hessenberg-Triangular Form is presented. This condensed Form Q T (A,B)Z = (H,T), where H and T axe block upper Hessenberg and upper Triangular, respectively, and Q and Z orthogonal, may serve as a first step in the solution of the generalized eigenvalue problem Ax = λBx. It is shown how an elementwise algorithm can be reorganized in terms of blocked factorizations and higher level BLAS operations. Several ways to annihilate elements are compared. Specifically, the use of Givens rotations, Householder transFormations, and combinations of the two. PerFormance results of the different variants are presented and compared to the LAPACK implementation DGGHRD, which indeed is unblocked.
