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Order Reduction in z-Domain for Interval System Using an Arithmetic Operator

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Abstract

This paper deals with order reduction in discrete-time systems. The reduction technique is based on utilization of Routh approximation and multiplicative operator. Various combinations of Routh table are used to derive the desired numerator and denominator polynomial of reduced-order model. Numerical examples are presented to verify the proposed algorithm.

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References

  1. A. Chandel, M.K. Sharma, D. Parashar, Mixed algorithm for large scale uncertain discrete interval models, in Proceedings of IEEE Uttar Pradesh Section International Conference on Electrical, Computer and Electronics Engineering (UPCON) (2016), pp. 400–403

  2. A.K. Choudhary, S.K. Nagar, Direct truncation method for order reduction of discrete-interval system, in Proceedings of Annual IEEE India Conference (IEEE, Mumbai, India, 2013), pp. 1–4

  3. A.K. Choudhary, S.K. Nagar, Gamma Delta approximation for reduction of discrete-interval system, in Proceedings of International Conference on Advanced Recent Technology Electrical and Electronics (Institute of Doctors Engineers and Scientists, Bangalore, India, 2013), pp. 91–94

  4. B.R. Barmish, A generalization of Kharitonov’s four-polynomial concept for robust stability problems with linearly dependent coefficient perturbations. IEEE Trans. Automat. Contr. 34, 157–165 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  5. Y. Choo, Suboptimal bilinear Routh approximant for discrete systems. J. Dyn. Syst. Meas. Control 128, 742–745 (2006)

    Article  Google Scholar 

  6. A.K. Choudhary, S.K. Nagar, Order reduction techniques via Routh approximation: a critical survey. IETE J. Res. (2018). https://doi.org/10.1080/03772063.2017.1419836

    Google Scholar 

  7. J. Cieslik, On possibilities of the extension of Kharitonov’s stability test for interval polynomials to the discrete-time case. IEEE Trans. Automat. Contr. 32, 237–238 (1987)

    Article  MathSciNet  Google Scholar 

  8. Y. Dolgin, E. Zeheb, Model reduction of uncertain FIR discrete-time systems. IEEE Trans. Circuits Syst. II Express Briefs 51, 406–411 (2004)

    Article  Google Scholar 

  9. B. Gayatri, K.K. Kumar, A.V.S. Lakshmi, V.S. Karteek, Uncertain systems order reduction by aggregation method. Int. J. Electr. Comput. Eng. 7(1), 244–252 (2017)

    Google Scholar 

  10. C.-C. Hsu, W.-Y. Wang, Discrete modelling of uncertain continuous systems having an interval structure using higher-order integrators. Int. J. Syst. Sci. 31, 467–477 (2000)

    Article  MATH  Google Scholar 

  11. C. Hwang, Y.C. Lee, A new family of Routh approximants. Circuits Syst. Signal Process. 16, 1–25 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  12. C. Hwang, S.F. Yang, Comments on the computation of interval Routh approximants. IEEE Trans. Automat. Control 44, 1782–1787 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  13. O. Ismail, B. Bandyopadhyay, R. Gorez, Discrete interval system reduction using Pade approximation to allow retention of dominant poles. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 44, 1075–1078 (1997)

    Article  MathSciNet  Google Scholar 

  14. M.S. Kumar, G. Begum, Model order reduction of linear time interval system using stability equation method and a soft computing technique. Adv. Electr. Electron. Eng. 14(2), 153–161 (2016)

    Google Scholar 

  15. K.K. Kumar, S. Kurman, Analysis and design of high order discrete time interval systems using new order reduction technique via least squares method and time moments technique. Int. J. Res. Appl. Sci. Eng. Technol. 6(2), 562–569 (2018)

    Article  Google Scholar 

  16. L. Li, Coprime factor model reduction for discrete-time uncertain systems. Syst. Control Lett. 74, 108–114 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  17. R.E. Moore, E. Moore, Interval Analysis, i (Prentice-Hall, Englewood Cliffs, 1966)

    MATH  Google Scholar 

  18. R.E. Moore, R.B. Kearfott, M.J. Cloud, Introduction to Interval Analysis (Society for Industrial and Applied Mathematics, Philadelphia, 2009)

    Book  MATH  Google Scholar 

  19. N. Gupta, A. Narain, Reduction of discrete interval systems through Fuzzy-c means clustering with dominant pole retention, in Proceedings of 5th Australian Control Conference (AUCC). (2015), pp. 348–353

  20. O. Ismail, On multipoint Pade approximation for discrete interval systems, in Proceedings of 28th Southeast Symposium System Theory (IEEE Computer Society Press, 1996), pp. 497–501

  21. D.J.M. Prasad, M.S. Kumar, Model order reduction of discrete time interval system using improved bilinear Routh approximation. J. Sci. Eng. Technol. Res. 5(1), 90–94 (2016)

    Google Scholar 

  22. Ruchira, An approximation technique for order reduction of interval system, in Proceedings of International Conference Recent Device Control Automation Power Engineering (2015), pp. 346–349

  23. C.N. Sandhya, M.S. Kumar, Evolutionary algorithm and fuzzy c-means clustering based order reduction of discrete time interval systems. J. Pure Appl. Math. 114(8), 309–319 (2017)

    Google Scholar 

  24. G.V.K.R. Sastry, G.R. Rao, P.M. Rao, Large scale interval system modelling using Routh approximants. Electron. Lett. 36, 768 (2000)

    Article  Google Scholar 

  25. L. Zhang, P. Shi, E.-K. Boukas, C. Wang, H ∞ model reduction for uncertain switched linear discrete-time systems. Automatica 44, 2944–2949 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  26. L. Zhang, E.-K. Boukas, P. Shi, μ-dependent model reduction for uncertain discrete-time switched linear systems with average dwell time. Int. J. Control 82, 378–388 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  27. U. Zulfiqar, M. Liaquat, Model reduction of discrete-time systems in limited interval. Turk. J. Electr. Eng. Comput. Sci. 26, 294–306 (2018)

    Article  Google Scholar 

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Author notes

  1. Amit Kumar Choudhary

    Present address: Department of Electrical Engineering, BIT Sindri, Dhanbad, Jharkhand, 828123, India

Authors and Affiliations

  1. Department of Electrical Engineering, Indian Institute of Technology (Banaras Hindu University) Varanasi, Varanasi, U.P., 221005, India

    Amit Kumar Choudhary & Shyam Krishna Nagar

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  1. Amit Kumar Choudhary
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  2. Shyam Krishna Nagar
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Correspondence to Amit Kumar Choudhary.

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Choudhary, A.K., Nagar, S.K. Order Reduction in z-Domain for Interval System Using an Arithmetic Operator. Circuits Syst Signal Process 38, 1023–1038 (2019). https://doi.org/10.1007/s00034-018-0912-7

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