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59
Modelica  a language for physical system modeling, visualization and interaction
 In 1999 IEEE Symposium on ComputerAided Control System Design
, 1999
"... Modelica is an objectoriented language for modeling of large, complex and heterogeneous physical systems. It is suited for multidomain modeling, for example for modeling of mechatronics including cars, aircrafts and industrial robots which typically consist of mechanical, electrical and hydraulic ..."
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Cited by 27 (3 self)
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Modelica is an objectoriented language for modeling of large, complex and heterogeneous physical systems. It is suited for multidomain modeling, for example for modeling of mechatronics including cars, aircrafts and industrial robots which typically consist of mechanical, electrical and hydraulic subsystems as well as control systems. General equations are used for modeling of the physical phenomena. No particular variable needs to be solved for manually. A Modelica tool will have enough information to do that automatically. The language has been designed to allow tools to generate efficient code automatically. The modeling effort is thus reduced considerably since model components can be reused and tedious and errorprone manual manipulations are not needed. The principles of objectoriented modeling and the details of the Modelica language as well as several examples are presented. 1.
Nonlinear eigenvalue problems: A challenge for modern eigenvalue methods, GAMMReports
"... We discuss the state of the art in numerical solution methods for large scale polynomial or rational eigenvalue problems. We present the currently available solution methods such as the JacobiDavidson, Arnoldi or the rational Krylov method and analyze their properties. We briefly introduce a new li ..."
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Cited by 26 (2 self)
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We discuss the state of the art in numerical solution methods for large scale polynomial or rational eigenvalue problems. We present the currently available solution methods such as the JacobiDavidson, Arnoldi or the rational Krylov method and analyze their properties. We briefly introduce a new linearization technique and demonstrate how it can be used to improve structure preservation and with this the accuracy and efficiency of linearization based methods. We present several recent applications where structured and unstructured nonlinear eigenvalue problems arise and some numerical results.
Model Reduction Software in the SLICOT Library
 Applied and Computational Control, Signals, and Circuits, volume 629 of The Kluwer International Series in Engineering and Computer Science
, 2000
"... We describe the model reduction software developed recently for the control and systems library SLICOT. Besides a powerful collection of Fortran 77 routines implementing the last algorithmic developments for several wellknown balancing related methods, we also describe model reduction tools develop ..."
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Cited by 23 (5 self)
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We describe the model reduction software developed recently for the control and systems library SLICOT. Besides a powerful collection of Fortran 77 routines implementing the last algorithmic developments for several wellknown balancing related methods, we also describe model reduction tools developed to facilitate the usage of SLICOT routines in user friendly environments like Matlab or Scilab. Extensive testing of the implemented tools has been done using both special benchmark problems as well as models of several complex industrial plants. Testing results and performance comparisons show the superiority of SLICOT model reduction tools over existing model reduction software.
A Descriptor Systems Toolbox for MATLAB
 Proc. CACSD’2000 Symposium
, 2000
"... We describe a recently developed Descriptor Systems Toolbox implemented under Matlab. This Toolbox relies on the object oriented approach for control systems analysis and design provided within the standard Control Toolbox of Matlab. The basic approach to develop the Descriptor Systems Toolbox was ..."
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Cited by 18 (10 self)
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We describe a recently developed Descriptor Systems Toolbox implemented under Matlab. This Toolbox relies on the object oriented approach for control systems analysis and design provided within the standard Control Toolbox of Matlab. The basic approach to develop the Descriptor Systems Toolbox was to exploit the powerful matrix and system object manipulation features of Matlab via flexible and functionally rich high level mfunctions, while simultaneously enforcing highly e#cient and numerically sound structure exploiting computations via the mexfunction technology of Matlab to solve critical numerical problems. The mexfunctions are based on Fortran codes from Lapack and Slicot.
Fortran 77 subroutines for computing the eigenvalues of Hamiltonian matrices II
, 2004
"... This article describes Fortran 77 subroutines for computing eigenvalues and invariant subspaces of Hamiltonian and skewHamiltonian matrices. The implemented algorithms are based on orthogonal symplectic decompositions, implying numerical backward stability as well as symmetry preservation for the c ..."
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Cited by 13 (4 self)
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This article describes Fortran 77 subroutines for computing eigenvalues and invariant subspaces of Hamiltonian and skewHamiltonian matrices. The implemented algorithms are based on orthogonal symplectic decompositions, implying numerical backward stability as well as symmetry preservation for the computed eigenvalues. These algorithms are supplemented with balancing and block algorithms, which can lead to considerable accuracy and performance improvements. As a byproduct, an efficient implementation for computing symplectic QR decompositions is provided. We demonstrate the usefulness of the subroutines for several, practically relevant examples.
Mechanical Derivation and Systematic Analysis of Correct Linear Algebra Algorithms
, 2006
"... We consider the problem of developing formally correct dense linear algebra libraries. The problem would be solved convincingly if, starting from the mathematical speciﬁcation of a target operation, it were possible to generate, implement and analyze a family of correct algorithms that compute the o ..."
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Cited by 12 (3 self)
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We consider the problem of developing formally correct dense linear algebra libraries. The problem would be solved convincingly if, starting from the mathematical speciﬁcation of a target operation, it were possible to generate, implement and analyze a family of correct algorithms that compute the operation. This thesis presents evidence that for a class of dense linear operations, systematic and mechanical development of algorithms is within reach. It describes and demonstrates an approach for deriving and implementing, systematically and even mechanically, proven correct algorithms. It also introduces a systematic procedure to analyze, in a modular fashion, numerical properties of the generated algorithms.
The sensitivity of computational control problems
 IEEE Control Syst. Mag
, 2004
"... What factors contribute to the accurate and efficient numerical solution of problems in control systems analysis and design? Although numerical methods have been used for many centuries to solve problems in science and engineering, the importance of computation grew tremendously with the advent of d ..."
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Cited by 12 (2 self)
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What factors contribute to the accurate and efficient numerical solution of problems in control systems analysis and design? Although numerical methods have been used for many centuries to solve problems in science and engineering, the importance of computation grew tremendously with the advent of digital computers. It became immediately clear that many of the classical analytical and numerical methods and algorithms could not be implemented directly as computer codes, although they were well suited for hand computations. What was the reason? When doing computations by hand a person can choose the accuracy of each elementary calculation and then estimate, based on intuition and experience, its influence on the final result. In contrast, when computations are done automatically, intuitive error control is usually not possible and the effect of errors on the intermediate calculations must be estimated in a more systematic way. Due to this observation, starting
Factorized solution of Lyapunov equations based on hierarchical matrix arithmetic
, 2006
"... We investigate the numerical solution of largescale Lyapunov equations with the sign function method. Replacing the usual matrix inversion, addition, and multiplication by formatted arithmetic for hierarchical matrices, we obtain an implementation that has linearpolylogarithmic complexity and memor ..."
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Cited by 12 (6 self)
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We investigate the numerical solution of largescale Lyapunov equations with the sign function method. Replacing the usual matrix inversion, addition, and multiplication by formatted arithmetic for hierarchical matrices, we obtain an implementation that has linearpolylogarithmic complexity and memory requirements. The method is well suited for Lyapunov operators arising from FEM and BEM approximations to elliptic differential operators. With the sign function method it is possible to obtain a lowrank approximation to a fullrank factor of the solution directly. The task of computing such a factored solution arises, e.g., in model reduction based on balanced truncation. The basis of our method is a partitioned Newton iteration for computing the sign function of a suitable matrix, where one part of the iteration uses formatted arithmetic while the other part directly yields approximations to the fullrank factor of the solution. We discuss some variations of our method and its application to generalized Lyapunov equations. Numerical experiments show that the method can be applied to problems of order up to O(10 5) on workstations.
Minimal statespace realization in linear system theory: An overview
 JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
, 2000
"... ..."
Robust numerical methods for robust control
 INSTITUT FÜR MATHEMATIK, TU BERLIN, STR. DES 17. JUNI 136, D10623
, 2004
"... We present numerical methods for the solution of the optimal H∞ control problem. In particular, we investigate the iterative part often called the γiteration. We derive a method with better robustness in the presence of rounding errors than other existing methods. It remains robust in the presence ..."
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Cited by 9 (7 self)
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We present numerical methods for the solution of the optimal H∞ control problem. In particular, we investigate the iterative part often called the γiteration. We derive a method with better robustness in the presence of rounding errors than other existing methods. It remains robust in the presence of rounding errors even as γ approaches its optimal value. For the computation of a suboptimal controller, we avoid solving algebraic Riccati equations with their problematic matrix inverses and matrix products by adapting recently suggested methods for the computation of deflating subspaces of skewHamiltonian/Hamiltonian pencils. These methods are applicable even if the pencil has eigenvalues on the imaginary axis. We compare the new method with older methods and present several examples.