Skip to main content

Model Order Reduction of Time Interval System: A Survey

  • Conference paper
  • First Online:
Proceedings of the Third International Conference on Soft Computing for Problem Solving

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 259))

Abstract

The Complexity of higher order linear systems are large and order of matrices are higher. Matrices of higher order are difficult to deal with. The main objectives of order reduction is to design a controller of lower order which can effectively control the original high order system so that the overall system is of lower order and easy to understand. Analysis and design of reduced order model becomes simpler and economic. Parametric uncertainties exist in practical systems for entire range of the operating conditions. To overcome this, time interval system is employed. This paper presents a survey on design of reduced order model for large scale time interval systems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Kumar, M., Gupta, R.: Design of decentralized PSSs for multi machine power system via reduced order model. In: 4th IEEE international conference on computational intelligence and communication networks (CICN), pp. 617–621 (2012)

    Google Scholar 

  2. Singh, V.P., Chandra, D.: Routh approximation based model reduction using series expansion of interval systems. In: IEEE International conference on power, control & embedded systems (ICPCES), vol 1, pp. 1–4 (2010)

    Google Scholar 

  3. Hansen, E.: Interval arithmetic in matrix computations. Part I, SIAM J. Num.Anal. 2, 308–320 (1965)

    MATH  Google Scholar 

  4. Gutman, P.O., Mannerfelt, C.F., Molander, P.: Contributions to the model reduction problem. IEEE Trans. Autom. Control 27(2), 454–455 (1982)

    Article  MATH  Google Scholar 

  5. Saini, D.K., Prasad, R.: Mixed evolutionary techniques to reduce order of linear interval systems using generlized routh array. Int. J. Eng. Sci. Technol. 2(10), 51976–55205 (2010)

    Google Scholar 

  6. Kumar, D.K., Nagar, S.K., Tiwari, J.P.: A new algorithm for model order reduction of interval systems. Bonfring Int. J. Data Min. 3(1), 6 (2013)

    Article  Google Scholar 

  7. Kumar, D.K., Nagar, S.K., Tiwari, J.P.: Model order reduction of interval systems using modified Routh approximation and factor division method. In: 35th national system conference (NSC), IIT Bhubaneswar, India (2011)

    Google Scholar 

  8. Kumar, D.K., Nagar, S.K., Tiwari, J.P.: Model order reduction of interval systems using mihailov criterion and routh approximations. Int. J. Eng. Sci. Technol. (IJEST) 3(7), 5593–5598 (2011)

    Google Scholar 

  9. Kumar, D.K., Nagar, S.K., Tiwari, J.P.: Model order reduction of interval systems using mihailov criterion and factor division method. Int. J. Comput. Appl. (IJCA) 28(11), 4–8 (2011)

    Google Scholar 

  10. Bhattacharya, S.P.: Robust Stabilization Against Structured Perturbations. Lecture Notes in Control and Information Sciences. Springer, New York (1987)

    Book  Google Scholar 

  11. Bandyopadhyay, B., Upadhye, A., Ismail, O.: γ–δ Routh approximation for interval systems. IEEE Trans. Autom. Control 42(8), 1127–1130 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  12. Hwang, C., Yang, S.F.: Comments on the computations of interval Routh approximants. IEEE Trans. Autom. Control 44(9), 1782–1787 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  13. Ismail, O., Bandyopadhyay, B.: Model order reduction of linear interval systems using pade approximation. In: IEEE International Symposium on Circuit and Systems (1995)

    Google Scholar 

  14. Dolgin, Y., Zeheb, E.: On Routh pade model reduction of interval systems. IEEE Trans. Autom. Control 48(9), 1610–1612 (2003)

    Article  MathSciNet  Google Scholar 

  15. Bandyopadhyay, B., Sreeram, V., Shingare, P.: Stable γ–δ Routh approximation for interval systems using Kharitonov polynomials. Int. J. Inf. Syst Sci. 44(3), 348–361 (2008)

    MathSciNet  Google Scholar 

  16. Kumar, D.K., Nagar, S.K., Tiwari, J.P.: Model order reduction of interval systems using mihailov criterion and cauer second form. Int. J. Comput. Appl. 32(6), 17–21 (2011)

    Google Scholar 

  17. Saini, D.K., Prasad, R.: Order reduction of linear interval systems using genetic algorithm. Int. J. Eng. Technol. 2(5), 316–319 (2010)

    Google Scholar 

  18. Babu, T., Natarajan, P.: Design of robust pid controller using hybrid algorithm for reduced order interval system. Asian J. Sci. Res. 5(3), 108–120 (2012)

    Article  Google Scholar 

  19. Sastry, G.V.K., Raja Rao, G.R., Rao, P.M.: Large scale interval system modeling using Routh approximants. Electron. Lett. 36(8), 768 (2000)

    Article  Google Scholar 

  20. Saini, D.K., Prasad, R.: Order reduction of linear interval systems using particle swarm optimization. MIT Int, J. Elect. Instrum. Eng. 1(1), 16–19 (2011)

    Google Scholar 

  21. Kharitonov, V.L.: Asymptotic stability of an equilibrium position of a family of systems of linear differential equations. Differrential’nye Uravneniya 14, 2086–2088 (1978)

    MATH  MathSciNet  Google Scholar 

  22. Bandyopadhyay, B., Ismail, O., Gorez, R.: Routh pade approximation for interval systems. IEEE Trans. Autom. Control 39, 2454–2456 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  23. Saraswathi, G.: A mixed method for order reduction of interval systems. In: International Conference on Intelligent and Advanced Systems, pp. 1042–1046 (2007)

    Google Scholar 

  24. Dolgin, Y.: Author’s reply. IEEE Trans. Autom. Control 50(2), 274–275 (2007)

    Article  MathSciNet  Google Scholar 

  25. Singh,V.P., Chandra, D.: Model reduction of discrete interval system using dominant poles retention and direct series expansion method. In: IEEE 5th international power engineering and optimization conference (PEOCO), vol 1, pp. 27–30 (2011)

    Google Scholar 

  26. Choo, Y.: A note on discrete interval system reduction via retention of dominant poles. Int. J. Control Autom. Syst. 5(2), 208–211 (2007)

    Google Scholar 

  27. Kumar, D.K., Nagar, S.K., Tiwari, J.P.: Model order reduction of interval systems using Routh approximations and cauer second form. Int. J. Adv. Sci. Technol. (IJAST (2011)

    Google Scholar 

Download references

Acknowledgments

Siyaram Yadav sincerely acknowledge Mr. Mahendra Kumar, Assistant professor, Mewar University, Chittorgarh (Rajasthan, India) for his kind cooperation and consistent guidance during M.Tech Program.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mahendra Kumar .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer India

About this paper

Cite this paper

Kumar, M., Aman, Yadav, S. (2014). Model Order Reduction of Time Interval System: A Survey. In: Pant, M., Deep, K., Nagar, A., Bansal, J. (eds) Proceedings of the Third International Conference on Soft Computing for Problem Solving. Advances in Intelligent Systems and Computing, vol 259. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1768-8_25

Download citation

  • DOI: https://doi.org/10.1007/978-81-322-1768-8_25

  • Published:

  • Publisher Name: Springer, New Delhi

  • Print ISBN: 978-81-322-1767-1

  • Online ISBN: 978-81-322-1768-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics