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Journal articles on the topic 'Routh'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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1

ADAMEC, LADISLAV. "A ROUTE TO ROUTH — THE CLASSICAL SETTING." Journal of Nonlinear Mathematical Physics 18, no. 1 (2011): 87–107. http://dx.doi.org/10.1142/s1402925111001180.

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2

Adamec, Ladislav. "A Route to Routh—The Parametric Problem." Acta Applicandae Mathematicae 117, no. 1 (2011): 115–34. http://dx.doi.org/10.1007/s10440-011-9654-2.

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3

HOWARD, J. E. "Routh revisited." International Journal of Control 50, no. 3 (1989): 883–88. http://dx.doi.org/10.1080/00207178908953404.

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4

Jalnapurkar, Sameer M., Melvin Leok, Jerrold E. Marsden, and Matthew West. "Discrete Routh reduction." Journal of Physics A: Mathematical and General 39, no. 19 (2006): 5521–44. http://dx.doi.org/10.1088/0305-4470/39/19/s12.

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5

Grabowska, Katarzyna, and Paweƚ Urbański. "Geometry of Routh reduction." Journal of Geometric Mechanics 11, no. 1 (2019): 23–44. http://dx.doi.org/10.3934/jgm.2019002.

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6

Litvin, I. N., and Yu E. Boreisha. "Stochastic Routh-Hurwitz problem." Cybernetics and Systems Analysis 27, no. 4 (1992): 527–34. http://dx.doi.org/10.1007/bf01130362.

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7

Zahreddine, Ziad. "The generalized Routh array and a further simplification of the extended Routh array." Tamkang Journal of Mathematics 32, no. 2 (2001): 131–36. http://dx.doi.org/10.5556/j.tkjm.32.2001.355.

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The well-known Routh Array settles the problem of stability of systems of differential equations with rral coefficients. The Extended Routh Array (ERA) is the complex counterpart of the Routh Array and it settles the stability of these systems when the coefficients are complex. Since its construction, the ERA remained more of a theoretical achievement, than a practical tool to test the stability of linear systems. Some attempts were made to overcome the complexity of the ERA. The Modified Extended Routh Array (MERA) was then introduced and it reduced the burden of computations, but still it in

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8

LANGEROCK, BAVO, and MARCO CASTRILLÓN LÓPEZ. "ROUTH REDUCTION FOR SINGULAR LAGRANGIANS." International Journal of Geometric Methods in Modern Physics 07, no. 08 (2010): 1451–89. http://dx.doi.org/10.1142/s0219887810004907.

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This paper concerns the Routh reduction procedure for Lagrangians systems with symmetry. It differs from the existing results on geometric Routh reduction in the fact that no regularity conditions on either the Lagrangian L or the momentum map JL are required apart from the momentum being a regular value of JL. The main results of this paper are: the description of a general Routh reduction procedure that preserves the Euler–Lagrange nature of the original system and the presentation of a presymplectic framework for Routh reduced systems. In addition, we provide a detailed description and inte

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9

Hwang, Chyi, and Ching-Shieh Hsieh. "Order Reduction of Discrete-Time System Via Bilinear Routh Approximation." Journal of Dynamic Systems, Measurement, and Control 112, no. 2 (1990): 292–97. http://dx.doi.org/10.1115/1.2896138.

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In this paper, a method of combining the Routh approximation method with the bilinear transformation is presented for deriving stable reduced-order models of a strictly proper z-transfer function Gn(z). It is based on applying the bilinear transformation to the (z+1)Gn(z), and then deriving a new bilinear Routh γ − δ canonical expansion for Gn(z). The proposed bilinear Routh approximation method has all the advantages of the Routh approximation method [5] while without having initial-value problem caused by the bilinear transformation. A numerical example is included to illustrate the procedur

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10

Byrne, Peter C. "On The Routh-Hurwitz Criterion." International Journal of Electrical Engineering & Education 33, no. 2 (1996): 157–64. http://dx.doi.org/10.1177/002072099603300205.

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On the Routh-Hurwitz criterion The ‘ε method’ of Routh-Hurwitz criterion is examined. When roots occur on the imaginary axis it is found necessary to take the limit as c goes to zero, after each row is completed, to check for the occurrence of a row of zeros.

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11

Bizyaev, I. A., and A. V. Tsiganov. "On the Routh sphere problem." Journal of Physics A: Mathematical and Theoretical 46, no. 8 (2013): 085202. http://dx.doi.org/10.1088/1751-8113/46/8/085202.

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12

Capriotti, S. "Routh reduction and Cartan mechanics." Journal of Geometry and Physics 114 (April 2017): 23–64. http://dx.doi.org/10.1016/j.geomphys.2016.11.015.

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13

Zhang, Kun, Hua Wang, and Hui Tao Wang. "Control of a Fractional-Order Arneodo System." Advanced Materials Research 383-390 (November 2011): 4405–12. http://dx.doi.org/10.4028/www.scientific.net/amr.383-390.4405.

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In this work, stability analysis of the Fractional-Order Arneodo system is studied by using the fractional Routh-Hurwitz criteria. Furthermore, the fractional Routh-Hurwitz conditions are used to control chaos in the proposed fractional-order system to its equilibria. Based on the fractional Routh-Hurwitz conditions and using specific choice of linear feedback controllers, it is shown that the Arneodo system is controlled to its equilibrium points. Numerical results show the effectiveness of the theoretical analysis.

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14

MORISUE, Toshiya. "An Elementary Proof of the Routh-Hurwitz Stability Criterion." Transactions of the Society of Instrument and Control Engineers 22, no. 4 (1986): 473–75. http://dx.doi.org/10.9746/sicetr1965.22.473.

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15

Zahreddine, Ziad. "On the interlacing property and the Routh-Hurwitz criterion." International Journal of Mathematics and Mathematical Sciences 2003, no. 12 (2003): 727–37. http://dx.doi.org/10.1155/s0161171203205287.

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Unlike the Nyquist criterion, root locus, and many other stability criteria, the well-known Routh-Hurwitz criterion is usually introduced as a mechanical algorithm and no attempt is made whatsoever to explain why or how such an algorithm works. It is widely believed that simple derivations of this important criterion are highly requested by the mathematical community. In this paper, we address this problem and provide a simple proof of the Routh-Hurwitz criterion based on two generalizations of an interesting property known in stability theory as the interlacing property. Within the same conte

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16

Cerwinka, Wolfgang H. "Response to commentary by Jonathan Routh." Journal of Pediatric Urology 9, no. 1 (2013): 56. http://dx.doi.org/10.1016/j.jpurol.2012.01.013.

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17

Kahoraho, E., J. L. Gutierrez, and S. Dormido. "Inversion algorithm to construct Routh approximants." Electronics Letters 21, no. 10 (1985): 424–26. http://dx.doi.org/10.1049/el:19850302.

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18

Hwang, C., T. Y. Guo, and J. H. Hwang. "Multifrequency Routh approximants for linear systems." IEE Proceedings - Control Theory and Applications 142, no. 4 (1995): 351–58. http://dx.doi.org/10.1049/ip-cta:19951882.

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19

Lamba, S., and B. Bandyopadhyay. "An improvement on Routh approximation technique." IEEE Transactions on Automatic Control 31, no. 11 (1986): 1047–50. http://dx.doi.org/10.1109/tac.1986.1104171.

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20

Bandyopadhyay, B., O. Ismail, and R. Gorez. "Routh-Pade approximation for interval systems." IEEE Transactions on Automatic Control 39, no. 12 (1994): 2454–56. http://dx.doi.org/10.1109/9.362850.

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21

Vilbe, P., L. C. Calvez, M. Sevellec, and C. Nouet. "I2-optimal numerator via Routh table." Electronics Letters 28, no. 14 (1992): 1306. http://dx.doi.org/10.1049/el:19920830.

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22

Cheng, Daizhan, and T. J. Tarn. "Control Routh Array And Its Applications." Asian Journal of Control 5, no. 1 (2008): 132–42. http://dx.doi.org/10.1111/j.1934-6093.2003.tb00104.x.

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23

Choo, Younseok. "Improvement to modified Routh approximation method." Electronics Letters 35, no. 7 (1999): 606. http://dx.doi.org/10.1049/el:19990363.

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24

Zenkov, D. V. "The geometry of the Routh problem." Journal of Nonlinear Science 5, no. 6 (1995): 503–19. http://dx.doi.org/10.1007/bf01209025.

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25

Ren, HaiGang, YingZheng Liu, and HanPin Chen. "Calculation of Routh Sea Surface Reflection." International Journal of Infrared and Millimeter Waves 27, no. 7 (2006): 1019–26. http://dx.doi.org/10.1007/s10762-006-9087-6.

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26

Hwang, Chyi, and Ying Chin Lee. "A new family of Routh approximants." Circuits Systems and Signal Processing 16, no. 1 (1997): 1–25. http://dx.doi.org/10.1007/bf01183172.

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27

Li, XianHong, HaiBin Yu та MingZhe Yuan. "Design of Optimal PID Controller withɛ-Routh Stability for Different Processes". Mathematical Problems in Engineering 2013 (2013): 1–22. http://dx.doi.org/10.1155/2013/582879.

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This paper presents a design method of the optimal proportional-integral-derivative (PID) controller withɛ-Routh stability for different processes through Lyapunov approach. The optimal PID controller could be acquired by minimizing an augmented integral squared error (AISE) performance index which contains control error and at least first-order error derivative, or even may containnth-order error derivative. The optimal control problem could be transformed into a nonlinear constraint optimization (NLCO) problem via Lyapunov theorems. Therefore, optimal PID controller could be obtained by solv

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28

Tamaji, Tamaji. "Desain Power System Stabilizer Berbasis Fuzzy dan Particle Swarm Optimization." Jurnal Intake : Jurnal Penelitian Ilmu Teknik dan Terapan 10, no. 1 (2019): 1–8. http://dx.doi.org/10.32492/jintake.v10i1.789.

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One important factor to produce qualified electricity is the stability of the system. An unstable system resulted in an undamped oscilation of system, and the stable system can damp the oscilation quickly. Therefore, it is necessary to apply a stability device to a power system and it is called a Power System Stabilizer (PSS). One of stability design is a feedback control design. Here, in this research, the state feedback control is designed for Single Machine Infinite Bus (SMIB) . The SMIB model is non-linear therefore the feedback control can’t be designed directly. Some researchers do linea

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29

Tamaji. "Desain Power System Stabilizer Berbasis Fuzzy dan Particle Swarm Optimization." Jurnal Intake : Jurnal Penelitian Ilmu Teknik dan Terapan 10, no. 1 (2019): 1–8. http://dx.doi.org/10.48056/jintake.v10i1.47.

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One important factor to produce a qualified electricity is the stability of the system. An unstable system resulted an undamped oscilation of system, and the stable system can damp the oscilation quickly. Therefore, it is necessary to apply a stability device to a power system and it is called a Power System Stabilizer (PSS). One of stability design is a feedback control design. Here, in this research, the state feedback control are designed for Single Machine Infinite Bus (SMIB) . The SMIB model is non linear therefore the feedback control can’t be designed directly. Some researchers do linea

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30

Fu, Jing-Li, Lijun Zhang, Chaudry Khalique, and Ma-Li Guo. "Circulatory integral and Routh's equations of Lagrange systems with Riemann-Liouville fractional derivatives." Thermal Science 25, no. 2 Part B (2021): 1355–63. http://dx.doi.org/10.2298/tsci200520034f.

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In this paper, the circulatory integral and Routh?s equations of Lagrange systems are established with Riemann-Liouville fractional derivatives, and the circulatory integral of Lagrange systems is obtained by making use of the relationship between Riemann-Liouville fractional integrals and fractional derivatives. Thereafter, the Routh?s equations of Lagrange systems are given based on the fractional circulatory integral. Two examples are presented to illustrate the application of the results.

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31

Holtz, Olga. "Hermite–Biehler, Routh–Hurwitz, and total positivity." Linear Algebra and its Applications 372 (October 2003): 105–10. http://dx.doi.org/10.1016/s0024-3795(03)00501-9.

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32

Choo, Younseok. "Suboptimal Bilinear Routh Approximant for Discrete Systems." Journal of Dynamic Systems, Measurement, and Control 128, no. 3 (2004): 742–45. http://dx.doi.org/10.1115/1.2234495.

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Recently an improved bilinear Routh approximation method has been suggested for the order reduction of discrete systems. In the method, the last α and β parameters of a reduced model were replaced by new parameters so that the impulse response energy of an original system is also preserved in the reduced model without destroying the stability preserving and time-moments matching properties. In this paper a new and simple improvement is proposed from which one can find a suboptimal bilinear Routh approximant. Compared to the previous result, the approach of this paper has an advantage that the

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33

Landers, R. "An interesting fact regarding the Routh table." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 223, no. 5 (2009): 709–11. http://dx.doi.org/10.1243/09596518jsce707.

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The Routh table is a powerful analysis tool used to determine how many roots of a given polynomial have negative, zero, and positive real parts. A special case occurs when a row of zeros is encountered. This indicates an even polynomial may be factored from the given polynomial. It is well known that the even polynomial is in the row above the row of zeros. In this technical note it will be shown that the even polynomial may be factored from all of the polynomials in the rows above the row of zeros.

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34

孙, 右烈. "标准化的Routh方程". Chinese Science Bulletin 34, № 18 (1989): 1436–37. http://dx.doi.org/10.1360/csb1989-34-18-1436.

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35

Bandyopadhyay, B., Avinash Upadhye та Osman Ismail. "γ-δ Routh approximation for interval systems". IEEE Transactions on Automatic Control 42, № 8 (1997): 1127–30. http://dx.doi.org/10.1109/9.618241.

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36

Ferrante, A., A. Lepschy, and U. Viaro. "A simple proof of the Routh test." IEEE Transactions on Automatic Control 44, no. 6 (1999): 1306–9. http://dx.doi.org/10.1109/9.769396.

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37

Marsden, Jerrold E., Tudor S. Ratiu, and Jürgen Scheurle. "Reduction theory and the Lagrange–Routh equations." Journal of Mathematical Physics 41, no. 6 (2000): 3379–429. http://dx.doi.org/10.1063/1.533317.

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38

František Marko and Semyon Litvinov. "On the Steiner–Routh Theorem for Simplices." American Mathematical Monthly 124, no. 5 (2017): 422. http://dx.doi.org/10.4169/amer.math.monthly.124.5.422.

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39

Kim, Byungsoo. "Routh symmetry in the Chaplygin’s rolling ball." Regular and Chaotic Dynamics 16, no. 6 (2011): 663–70. http://dx.doi.org/10.1134/s1560354711060074.

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40

Choo, Younseok. "Direct method for obtaining modified Routh approximants." Electronics Letters 35, no. 19 (1999): 1627. http://dx.doi.org/10.1049/el:19991135.

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41

García-Toraño Andrés, Eduardo, Tom Mestdag, and Hiroaki Yoshimura. "Implicit Lagrange–Routh equations and Dirac reduction." Journal of Geometry and Physics 104 (June 2016): 291–304. http://dx.doi.org/10.1016/j.geomphys.2016.02.010.

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42

Lepschy, A., G. A. Mian, and U. Viaro. "A Geometrical Interpretation of the Routh Test." Journal of the Franklin Institute 325, no. 6 (1988): 695–703. http://dx.doi.org/10.1016/0016-0032(88)90003-8.

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43

Sigal, Ron. "Algorithms for the Routh-Hurwitz stability test." Mathematical and Computer Modelling 13, no. 8 (1990): 69–77. http://dx.doi.org/10.1016/0895-7177(90)90072-u.

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44

Meinsma, Gjerrit. "Elementary proof of the Routh-Hurwitz test." Systems & Control Letters 25, no. 4 (1995): 237–42. http://dx.doi.org/10.1016/0167-6911(94)00089-e.

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45

Zhang Yi. "Routh method of reduction of Birkhoffian systems." Acta Physica Sinica 57, no. 9 (2008): 5374. http://dx.doi.org/10.7498/aps.57.5374.

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46

Mittal, Shailendra K., Dinesh Chandra, and Bharti Dwivedi. "VEGA Based Routh-Padé Approximants ForDiscrete Time Systems : A Computer-Aided Approach." International Journal of Engineering and Technology 1, no. 5 (2009): 424–29. http://dx.doi.org/10.7763/ijet.2009.v1.79.

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47

Handayani, Putri, Mahdhivan Syafwan, and Efendi . "PEMODELAN DAN ANALISIS KESTABILAN SISTEM MEMRISTOR KUBIK ORDE EMPAT." Jurnal Matematika UNAND 6, no. 3 (2017): 1. http://dx.doi.org/10.25077/jmu.6.3.1-6.2017.

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Abstrak. Pada penelitian ini, model sistem memristor kubik orde empat diformulasidari hukum sirkuit Kirchho dan hukum induksi Faraday dengan menggunakan memduktansiyang dikarakterisasi oleh fungsi kuadrat denit positif. Dengan menggunakankriteria Routh-Hurwitz, ditinjau kestabilan sistem di sekitar titik ekuilibrium. Hasil yangdiperoleh menunjukkan bahwa solusi sistem memristor kubik orde empat stabil. Beberapacontoh kasus yang diselesaikan secara numerik telah mengkonrmasi hasil analisistersebut.Kata Kunci: Memristor kubik orde empat, kriteria Routh-Hurwitz, hukum sirkuit Kirchho,hukum induks

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48

Li, Jia, Xinzhen Wu, Xibo Yuan, and Haifeng Wang. "Load Capacity Analysis of Self-Excited Induction Generators Based on Routh Criterion." Energies 12, no. 20 (2019): 3953. http://dx.doi.org/10.3390/en12203953.

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In this paper, the Routh criterion has been used to analyze the stability of a self-excited induction generator-based isolated system which is regarded as an autonomous system. Special focus has been given to the load capacity of the self-excited induction generator. The state matrix of self-excited induction generators with resistor-inductor load has been established based on transient equivalent circuits in the stator stationary reference-frame. The recursive Routh table of self-excited induction generators is established by the characteristic polynomial coefficients of the state matrix. Acc

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49

Sun, Ying, and Wei Yan. "Analyze a Feedback System with the R-H Stability Criterion." Applied Mechanics and Materials 496-500 (January 2014): 1698–701. http://dx.doi.org/10.4028/www.scientific.net/amm.496-500.1698.

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From a practical point of view, a closed-loop feedback system that is unstable is of little value. Many control systems are subject to extraneous disturbance signals that cause the system to provide an inaccurate output. The Routh-Hurwitz criterion ascertains the absolute stability of a system by determining whether any of the roots of the characteristic equation lie in the right half of the s-plane. This study concludes with a stability analysis based on the Routh-Hurwitz method.

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50

Hasnawati, Hasnawati, R. Ratianingsih, and J. W. Puspita. "ANALISIS KESTABILAN MODEL MATEMATIKA PADA PENYEBARAN KANKER SERVIKS MENGGUNAKAN KRITERIA ROUTH-HURWITZ." JURNAL ILMIAH MATEMATIKA DAN TERAPAN 14, no. 1 (2017): 120–27. http://dx.doi.org/10.22487/2540766x.2017.v14.i1.8360.

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