## SLICOT - A Subroutine Library in Systems and Control Theory (1997)

Venue: | Applied and Computational Control, Signals, and Circuits |

Citations: | 75 - 53 self |

### BibTeX

@INPROCEEDINGS{Benner97slicot-,

author = {Peter Benner and Volker Mehrmann and Vasile Sima and Sabine Van Huffel and Andras Varga},

title = {SLICOT - A Subroutine Library in Systems and Control Theory},

booktitle = {Applied and Computational Control, Signals, and Circuits},

year = {1997},

pages = {499--539},

publisher = {Birkhäuser}

}

### Years of Citing Articles

### OpenURL

### Abstract

This article describes the subroutine library SLICOT that provides Fortran 77 implementations of numerical algorithms for computations in systems and control theory. Around a nucleus of basic numerical linear algebra subroutines, this library builds methods for the design and analysis of linear control systems. A brief history of the library is given together with a description of the current version of the library and the on-going activities to complete and improve the library in several aspects. 1 Introduction Systems and control theory are disciplines widely used to describe, control, and optimize industrial and economical processes. There is now a huge amount of theoretical results available which has lead to a variety of methods and algorithms used throughout industry and academia. Although based on theoretical results, these methods often fail when applied to real-life problems, which often tend to be ill-posed or of high dimensions. This failing is frequently due to the lack of...

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Citation Context ...rent approach to this topic is to make use as far as possible of the established standard packages available for numerical linear algebra computations, i.e., the Basic Linear Algebra Subroutines BLAS =-=[25, 16, 15]-=- and the Linear Algebra Package LAPACK [2]. These libraries form the basic layer of SLICOT. On top of this, subroutines for the numerical solution of mathematical problems often encountered in CACSD a... |

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Citation Context ...ICOT version involves the extension of the SLICOT Standard [59] for high-performance computations on parallel architectures and the selection of standard communication kernels such as MPI [29] or PVM =-=[19]-=- and parallel numerical linear algebra libraries such as ScaLAPACK [8] or PLAPACK [38]. 7.3 Integration of software in a user-friendly environment The main aim of WGS is to see the library be used by ... |

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Citation Context ...rent approach to this topic is to make use as far as possible of the established standard packages available for numerical linear algebra computations, i.e., the Basic Linear Algebra Subroutines BLAS =-=[25, 16, 15]-=- and the Linear Algebra Package LAPACK [2]. These libraries form the basic layer of SLICOT. On top of this, subroutines for the numerical solution of mathematical problems often encountered in CACSD a... |

446 | An extended set of fortran basic linear algebra subprograms
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Citation Context ...rent approach to this topic is to make use as far as possible of the established standard packages available for numerical linear algebra computations, i.e., the Basic Linear Algebra Subroutines BLAS =-=[25, 16, 15]-=- and the Linear Algebra Package LAPACK [2]. These libraries form the basic layer of SLICOT. On top of this, subroutines for the numerical solution of mathematical problems often encountered in CACSD a... |

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Citation Context ...s possible of the established standard packages available for numerical linear algebra computations, i.e., the Basic Linear Algebra Subroutines BLAS [25, 16, 15] and the Linear Algebra Package LAPACK =-=[2]-=-. These libraries form the basic layer of SLICOT. On top of this, subroutines for the numerical solution of mathematical problems often encountered in CACSD are built such as linear and quadratic matr... |

353 |
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Citation Context ...h-performance computations on parallel architectures and the selection of standard communication kernels such as MPI [29] or PVM [19] and parallel numerical linear algebra libraries such as ScaLAPACK =-=[8]-=- or PLAPACK [38]. 7.3 Integration of software in a user-friendly environment The main aim of WGS is to see the library be used by as many scientists and engineers in industry as possible, so that the ... |

329 |
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Citation Context ... parallel SLICOT version involves the extension of the SLICOT Standard [59] for high-performance computations on parallel architectures and the selection of standard communication kernels such as MPI =-=[29]-=- or PVM [19] and parallel numerical linear algebra libraries such as ScaLAPACK [8] or PLAPACK [38]. 7.3 Integration of software in a user-friendly environment The main aim of WGS is to see the library... |

236 |
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Citation Context ... numerical linear algebra operations: solution of special linear systems (e.g., with triangular or complex upper Hessenberg matrices), total least squares using (partial) singular value decomposition =-=[43]-=-, etc. Another set of subroutines is included for algebraic operations involving scalar polynomials or polynomial matrices. Chapter S (Synthesis Routines) includes routines for the design of a system ... |

80 |
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Citation Context ...omputations on parallel architectures and the selection of standard communication kernels such as MPI [29] or PVM [19] and parallel numerical linear algebra libraries such as ScaLAPACK [8] or PLAPACK =-=[38]-=-. 7.3 Integration of software in a user-friendly environment The main aim of WGS is to see the library be used by as many scientists and engineers in industry as possible, so that the careful efforts ... |

75 |
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Citation Context ...ethods for the solution of periodic Lyapunov equations [48], descriptor systems analysis procedures [28], symplectic methods to solve Riccati equations [1, 4, 32], and subspace identification methods =-=[53, 44, 31]-=-. 3 Retrospect 3.1 Short history of control subroutine libraries The development of efficient, reliable, and portable numerical software requires joining expertise in theory, in numerical mathematics,... |

58 |
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Citation Context ...ns (AREs) can be solved in Matlabsusing the functions care for continuous-time systems and dare for discrete-time systems [26]. These are based on forming the deflating subspace approach described in =-=[3, 41]-=- and require the computation of the stable deflating subspace of the matrix pencils corresponding to the ARE. This is achieved by using the built-in implementation of the QZ algorithm in Matlab. We re... |

55 |
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Citation Context ...ns (AREs) can be solved in Matlabsusing the functions care for continuous-time systems and dare for discrete-time systems [26]. These are based on forming the deflating subspace approach described in =-=[3, 41]-=- and require the computation of the stable deflating subspace of the matrix pencils corresponding to the ARE. This is achieved by using the built-in implementation of the QZ algorithm in Matlab. We re... |

51 | A collection of benchmark examples for the numerical solution of algebraic riccati equations I: continuous-time case
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Citation Context ...accompany SLICOT with benchmark collections for each of the major problem areas. Currently, SLICOT contains two such benchmark collections in the areas of linear quadratic control (Riccati equations) =-=[5, 6, 7]-=-. Other collections are currently being developed. See the WGS homepage for details. 5 Contents of SLICOT 5.1 Current contents of the library A detailed presentation of the previous SLICOT Releases 1 ... |

44 |
Algorithms for Linear-Quadratic Optimization, volume 200 of Pure and Applied Mathematics
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Citation Context ...thods for model reduction [46], periodic Schur methods for the solution of periodic Lyapunov equations [48], descriptor systems analysis procedures [28], symplectic methods to solve Riccati equations =-=[1, 4, 32]-=-, and subspace identification methods [53, 44, 31]. 3 Retrospect 3.1 Short history of control subroutine libraries The development of efficient, reliable, and portable numerical software requires join... |

40 |
Contributions to the Numerical Solution of Algebraic Riccati Equations and Related Eigenvalue Problems
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Citation Context ...thods for model reduction [46], periodic Schur methods for the solution of periodic Lyapunov equations [48], descriptor systems analysis procedures [28], symplectic methods to solve Riccati equations =-=[1, 4, 32]-=-, and subspace identification methods [53, 44, 31]. 3 Retrospect 3.1 Short history of control subroutine libraries The development of efficient, reliable, and portable numerical software requires join... |

39 | Mehrmann V. A multishift algorithm for the numerical solution of algebraic Riccati equations
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Citation Context ...thods for model reduction [46], periodic Schur methods for the solution of periodic Lyapunov equations [48], descriptor systems analysis procedures [28], symplectic methods to solve Riccati equations =-=[1, 4, 32]-=-, and subspace identification methods [53, 44, 31]. 3 Retrospect 3.1 Short history of control subroutine libraries The development of efficient, reliable, and portable numerical software requires join... |

26 | Periodic Lyapunov equations: some applications and new algorithms
- Varga
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Citation Context ...l task with an approximate cost of 25(Nn) 3 operations. Efficient and numerically reliable algorithms based on the periodic Schur decomposition have been developed for the solution of these equations =-=[48]-=-. The associated cost is about 25Nn 3 operations and thus leaves the computational burden acceptable. It was shown that for all practical purposes the proposed periodic output feedback approach is a c... |

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Citation Context ...cent developments are: balancing-free square-root methods for model reduction [46], periodic Schur methods for the solution of periodic Lyapunov equations [48], descriptor systems analysis procedures =-=[28]-=-, symplectic methods to solve Riccati equations [1, 4, 32], and subspace identification methods [53, 44, 31]. 3 Retrospect 3.1 Short history of control subroutine libraries The development of efficien... |

15 |
The ANDECS Design Environment for Control Engineering. 12ti IFAC World Congress
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- 1993
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Citation Context ...le in SLICOT, and a user-friendly interactive module has been implemented in ANDECS 3 to allow the efficient manipulation of a huge amount of system data stored in the hierarchical database of ANDECS =-=[22]-=-. Satellite attitude control The control problem is to determine a simple controller which, making use of the periodicity of the earth magnetic field, ensures a stable operation of a satellite on an e... |

10 | Benchmarks for the numerical solution of algebraic Riccati equations
- Benner, Laub, et al.
- 1997
(Show Context)
Citation Context ...accompany SLICOT with benchmark collections for each of the major problem areas. Currently, SLICOT contains two such benchmark collections in the areas of linear quadratic control (Riccati equations) =-=[5, 6, 7]-=-. Other collections are currently being developed. See the WGS homepage for details. 5 Contents of SLICOT 5.1 Current contents of the library A detailed presentation of the previous SLICOT Releases 1 ... |

7 | Numerical methods and software tools for model reduction
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- 1994
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Citation Context ...bust software implementations will be available in the forthcoming release of SLICOT; see Section 5.3. Some of the most recent developments are: balancing-free square-root methods for model reduction =-=[46]-=-, periodic Schur methods for the solution of periodic Lyapunov equations [48], descriptor systems analysis procedures [28], symplectic methods to solve Riccati equations [1, 4, 32], and subspace ident... |

6 | Optimal output feedback control: a multi-model approach
- Varga
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Citation Context ...the simultaneous output feedback stabilization of an n = 24 order aeromechanic helicopter multi-model with N = 41 vertex systems corresponding to 41 operating conditions of the rotor speed and thrust =-=[47]-=-. Gradient search techniques were used to find a local minimum for a quadratic performance index. The computational problem to determine the optimal output feedback control of the multimodel system wa... |

5 |
RSYST - two complementary program libraries for concurrent control engineering
- RASP
- 1991
(Show Context)
Citation Context ...ly efficient algorithms. In the architecture of each CACSD platform we can explicitly identify and usually also access a basic computational layer consisting of subroutine libraries, RASP 4 in ANDECS =-=[21]-=-, SLICOT in EASY5, or intrinsic functions and function toolboxes (in Scilab, Matlab, and Xmath). This layer includes all computational routines for CACSD specific mathematical and control computations... |

5 |
N4SID: Two subspace algorithms for the identification of combined deterministic-stochastic systems
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- 1994
(Show Context)
Citation Context ...ethods for the solution of periodic Lyapunov equations [48], descriptor systems analysis procedures [28], symplectic methods to solve Riccati equations [1, 4, 32], and subspace identification methods =-=[53, 44, 31]-=-. 3 Retrospect 3.1 Short history of control subroutine libraries The development of efficient, reliable, and portable numerical software requires joining expertise in theory, in numerical mathematics,... |

5 | A computational approach for optimal periodic output feedback control
- Varga, Pieters
- 1996
(Show Context)
Citation Context ... attitude control The control problem is to determine a simple controller which, making use of the periodicity of the earth magnetic field, ensures a stable operation of a satellite on an earth orbit =-=[50]-=-. The satellite system is described by a continuous-time linear periodic state space model of order n = 4, with m = 1 control inputs and p = 2 measurable outputs. The continuous-time periodic problem ... |

4 | Towards a coordinated development of numerical CACSD software: the RASP/SLICOT compatibility concept
- Grubel, Varga, et al.
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Citation Context ...t library. This joint library is the first step towards a standard platform for computational tools. For the sake of this cooperation, the RASP/SLICOT mutual compatibility concept has been introduced =-=[23]-=-, which enables a coordinated development of both libraries leading to a reduction of software implementation and testing efforts without giving up the identity of the separate libraries. Part of this... |

4 |
a subroutine library in control and systems theory
- SLICOT
- 1991
(Show Context)
Citation Context ...ic flexibility to users, and on the use of rigorous implementation and documentation standards (see [57, 59]). The previous and present releases of SLICOT contain about 90 user-callable routines (see =-=[39, 36]-=- and Table 15 in Appendix A), related to analysis, modeling, transformation and synthesis of systems. Future extensions will cover routines for descriptor systems, model reduction and subspace identif... |

3 |
SYSLAB: An interactive system for analysis and design of linear multivariable systems
- Petkov, Konstantinov
- 1985
(Show Context)
Citation Context ... simulation of multivariable systems. Another East-European control library with name LISPACK was developed by a Bulgarian group from Sofia. This library is included in the interactive SYSLAB package =-=[30]-=-. x 3.2 Standard libraries RASP and SLICOT: present status Apparently, to date, only RASP and SLICOT are in active further development. The other initiatives failed to evolve due to a number of reason... |

3 | Algorithms and LAPACK-Based software for subspace identification
- Sima
- 1996
(Show Context)
Citation Context ...ethods for the solution of periodic Lyapunov equations [48], descriptor systems analysis procedures [28], symplectic methods to solve Riccati equations [1, 4, 32], and subspace identification methods =-=[53, 44, 31]-=-. 3 Retrospect 3.1 Short history of control subroutine libraries The development of efficient, reliable, and portable numerical software requires joining expertise in theory, in numerical mathematics,... |

3 | High-performance numerical software for control systems, and subspace-based system identification - Sima - 1997 |

3 |
BIMAS - a basic mathematical package for computer aided systems analysis and design
- Varga, Sima
- 1985
(Show Context)
Citation Context ... offers main programs for several chapters of control and systems theory and has found ample application in German industry. An interesting contribution from Romania is the mathematical library BIMAS =-=[51, 52]-=- which extends the capabilities of EISPACK and LINPACK. The control library BIMASC [45, 49] is based on BIMAS and provides many subroutines for analysis, modeling, design and simulation of multivariab... |

2 |
Integrated Scientific Computing with Scilab. Birkhauser
- Delebecque, Steer
- 1997
(Show Context)
Citation Context ... to solve periodic discrete-time Lyapunov equations. 2.3 Low level reusability of Fortran libraries Many sophisticated CACSD platforms available today like ANDECS [22], EASY5 [9], Matlab [27], Scilab =-=[11]-=-, or Xmath [24] rely on robust implementations of numerically reliable and computationally efficient algorithms. In the architecture of each CACSD platform we can explicitly identify and usually also ... |

2 |
Implementation and Documentation Standards for the Software Library
- Denham, Benson
- 1981
(Show Context)
Citation Context ...eration initiative, coordinated by Mike Denham at Kingston Polytechnic in the early eighties, led to the development of the control library SLICE which contains a set of almost 40 control ix routines =-=[13, 12]-=-. When this initiative stopped, the routines were further distributed by the Numerical Algorithms Group (NAG) from Oxford (UK) who issued a revised version of SLICE. In the same period, the Working Gr... |

2 |
BIMASC—A package of Fortran subprograms for analysis, modelling, design and simulation of control systems
- Varga, Davidoviciu
- 1985
(Show Context)
Citation Context ...e application in German industry. An interesting contribution from Romania is the mathematical library BIMAS [51, 52] which extends the capabilities of EISPACK and LINPACK. The control library BIMASC =-=[45, 49]-=- is based on BIMAS and provides many subroutines for analysis, modeling, design and simulation of multivariable systems. Another East-European control library with name LISPACK was developed by a Bulg... |

1 |
Educational aspects of development and application of a subprogram package for control
- Cellier, Grepper, et al.
- 1977
(Show Context)
Citation Context ...f complex interactive CACSD packages. Several efforts have been initiated in the past to develop such control libraries. The Scandinavian control library [17, 54] and the Swiss control library AUTLIB =-=[10]-=- were the first initiatives in the field. These libraries did not reach maturity, which illustrates the difficulties encountered by such a project. Another British cooperation initiative, coordinated ... |

1 |
A software library and interactive design environment for computer-aided control system design
- Denham
- 1985
(Show Context)
Citation Context ...eration initiative, coordinated by Mike Denham at Kingston Polytechnic in the early eighties, led to the development of the control library SLICE which contains a set of almost 40 control ix routines =-=[13, 12]-=-. When this initiative stopped, the routines were further distributed by the Numerical Algorithms Group (NAG) from Oxford (UK) who issued a revised version of SLICE. In the same period, the Working Gr... |

1 |
Scandinavian control library. Programming
- Elmqvist, Tysso, et al.
- 1976
(Show Context)
Citation Context ...ing blocks for the construction of all sorts of complex interactive CACSD packages. Several efforts have been initiated in the past to develop such control libraries. The Scandinavian control library =-=[17, 54]-=- and the Swiss control library AUTLIB [10] were the first initiatives in the field. These libraries did not reach maturity, which illustrates the difficulties encountered by such a project. Another Br... |

1 |
Benchmark problems for computer aided control system design
- Frederick
- 1988
(Show Context)
Citation Context ...es by means of this tool. 7.4 Benchmarking and testing the software in an industrial environment There is a definite need for more and adequate benchmarks for control methods and their implementation =-=[18]-=-. These benchmarks should be practically oriented. Carefully chosen benchmarks give insight in the state of the art with respect to the performance of methods in the language of the control system ana... |

1 |
Die regelungstechnische Programmbibliothek RASP
- Grubel
- 1983
(Show Context)
Citation Context ...R) and the resulting extension of routines in the SLICOT collection led to the second release of SLICOT in 1993 [36]. The development of the RASP library also started in the early eighties in Germany =-=[20]-=- and was partly based on the libraries EISPACK [34] and LINPACK [14]. Apart from routines, mostly for control, RASP also offers main programs for several chapters of control and systems theory and has... |

1 | Developments around the freeware standard control library SLICOT - Boom, Huffel - 1996 |

1 |
NICONET: network for performant numerical software development in control engineering
- Huffel, Boom
- 1997
(Show Context)
Citation Context ...b results, m = 1. Time Relative errors n AB01ND Matlab AB01ND 16 0.01 0.04 6.26e-16 32 0.01 0.14 4.16e-16 64 0.04 1.29 5.61e-16 128 0.30 25.55 1.09e-15 256 2.48 639.57 1.05e-15 (for more details, see =-=[60, 42]-=-). The expansion of the present WGS network (NICONET partners in the exploratory phase) to a European level is strongly encouraged in order to obtain a wider base of software developers and potential ... |

1 |
BIMASC - general description
- Varga
- 1983
(Show Context)
Citation Context ...e application in German industry. An interesting contribution from Romania is the mathematical library BIMAS [51, 52] which extends the capabilities of EISPACK and LINPACK. The control library BIMASC =-=[45, 49]-=- is based on BIMAS and provides many subroutines for analysis, modeling, design and simulation of multivariable systems. Another East-European control library with name LISPACK was developed by a Bulg... |

1 |
Scandinavian control library. A subroutine library in the field of automatic control
- Wieslander
- 1977
(Show Context)
Citation Context ...ing blocks for the construction of all sorts of complex interactive CACSD packages. Several efforts have been initiated in the past to develop such control libraries. The Scandinavian control library =-=[17, 54]-=- and the Swiss control library AUTLIB [10] were the first initiatives in the field. These libraries did not reach maturity, which illustrates the difficulties encountered by such a project. Another Br... |