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International Journal of Control Volume 53, 1991 - Issue 2
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Original Articles

Approximation of delay systems—a case study

C. GLADER Department of Mathematics, Åbo Akademi, Abo, 20500, Finland
,
G. HÖGNÄS Department of Mathematics, Åbo Akademi, Abo, 20500, Finland
,
P. M. MÄKILÄ Department of Chemical Engineering, Åbo Akademi, Abo, 20500, Finland.
&
H. T. TOIVONEN Department of Chemical Engineering, Åbo Akademi, Abo, 20500, Finland.
Pages 369-390 | Received 20 Sep 1989, Published online: 17 Apr 2007

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Xinhua Wang. (2022) Design and analysis of stable differentiator-predictor. International Journal of Control 95:5, pages 1228-1250.
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LUIS ANTONIO AGUIRRE. (1995) Matrix formulae for open and closed-loop approximate model matching in frequency domain. International Journal of Systems Science 26:11, pages 2069-2089.
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P. M. MÄKILÄT. (1991) Laguerre methods and H ∞ identification of continuous-time systems. International Journal of Control 53:3, pages 689-707.
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Sayan Chakraborty, Shanti Swaroop Kandala & C. P. Vyasarayani. (2019) Reduced ordered modelling of time delay systems using galerkin approximations and eigenvalue decomposition. International Journal of Dynamics and Control 7:3, pages 1065-1083.
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Giordano Scarciotti & Alessandro Astolfi. (2016) Model Reduction of Neutral Linear and Nonlinear Time-Invariant Time-Delay Systems With Discrete and Distributed Delays. IEEE Transactions on Automatic Control 61:6, pages 1438-1451.
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Egi Hidayat, Alexander Medvedev & Karin Nordström. (2013) Laguerre domain identification of the elementary motion detector model in insect vision. IFAC Proceedings Volumes 46:11, pages 623-628.
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Qi-Jie Zeng, Yun Zhang & Bin Tang. (2011) A bivector rotation approach to state feedback stabilization of linear time-invariant systems with input time delay. A bivector rotation approach to state feedback stabilization of linear time-invariant systems with input time delay.
Jonathan R. Partington. (2004) Some frequency-domain approaches to the model reduction of delay systems. Annual Reviews in Control 28:1, pages 65-73.
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Jean-Pierre Richard. (2003) Time-delay systems: an overview of some recent advances and open problems. Automatica 39:10, pages 1667-1694.
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Jonathan R. Partington. (2003) Some frequency-domain approaches to the model reduction of delay systems. IFAC Proceedings Volumes 36:19, pages 1-9.
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S H Al-Amer & F M Al-Sunni. (2016) H-infinity error bounds in approximating time-delay systems. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 217:5, pages 421-426.
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Carles Batlle & Alicia Miralles. (2000) On the approximation of delay elements by feedback. Automatica 36:5, pages 659-664.
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Angel Ribalta Stanford & Guillermo López Lagomasino. (2000) Approximation of Transfer Functions of Infinite Dimensional Dynamical Systems by Rational Interpolants with Prescribed Poles. Journal of Mathematical Analysis and Applications 244:1, pages 147-168.
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S.H. Al-Amer & F.M. Al-Sunni. (2000) Approximation of time-delay systems. Approximation of time-delay systems.
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P. M. Mäkilä & J. R. Partington. (1999) Shift Operator Induced Approximations of Delay Systems. SIAM Journal on Control and Optimization 37:6, pages 1897-1912.
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Y. Ohta. (1998) Further results on Hankel singular values and vectors of a class of infinite dimensional systems. Further results on Hankel singular values and vectors of a class of infinite dimensional systems.
Silviu-Iulian Niculescu, Erik I. Verriest, Luc Dugard & Jean-Michel Dion. 1998. Stability and Control of Time-delay Systems. Stability and Control of Time-delay Systems 1 71 .
M.G. Yoon & B.H. Lee. (1997) A new approximation method for time-delay systems. IEEE Transactions on Automatic Control 42:7, pages 1008-1012.
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Y. Ohta. (1997) Hankel singular values and vectors of a class of infinite dimensional systems for control and approximation problems. Hankel singular values and vectors of a class of infinite dimensional systems for control and approximation problems.
A. Beghi, A. Lepschy & U. Viaro. (1997) Approximating delay elements by feedback. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 44:9, pages 824-828.
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Xin Li. (1996) L/sup 1/ approximation of a certain class of infinite dimensional systems in time-domain. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 43:5, pages 397.
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B. Wahlberg & P.M. Mäkilä. (1996) On approximation of stable linear dynamical systems using Laguerre and Kautz functions. Automatica 32:5, pages 693-708.
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Y. Ohta & I Cheol Hwang. (1996) Hankel approximation of commensurate input delay systems. Hankel approximation of commensurate input delay systems.
R.F. Curtain & Yishao Zhou. (1996) A weighted mixed-sensitivity H/sub ∞/-control design for irrational transfer matrices. IEEE Transactions on Automatic Control 41:9, pages 1312-1321.
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A. Beghi, A. Lepschy & U. Viaro. 1996. Advanced Manufacturing Systems and Technology. Advanced Manufacturing Systems and Technology 617 624 .
Kenneth L. Bowers & John LundRuth F. Curtain & Yishao Zhou. 1995. Computation and Control IV. Computation and Control IV 99 113 .
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J. Lam. (1994) Analysis on the Laguerre formula for approximating delay systems. IEEE Transactions on Automatic Control 39:7, pages 1517-1521.
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Bo Wahlberg. (1994) Laguerre and Kautz Models. IFAC Proceedings Volumes 27:8, pages 965-976.
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Alphonse P. Magnus. 1994. Nonlinear Numerical Methods and Rational Approximation II. Nonlinear Numerical Methods and Rational Approximation II 173 185 .

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