IJRME – Volume 1 Issue 2 Paper 4


Author’s Name :  P Vivekanandan | P Kalaiselvi | V Padmaja | Prachi Singh Sengar | B Vinothini

Volume 01 Issue 02  Year 2014  ISSN No:  2349-3860  Page no: 14-18



Modeling physical systems are usually results in complex high-order dynamic models. It is necessary to reduce it to a lower order system. A mixed method is suggested for reducing order of the large scale interval systems. Kharitonov polynomial is employed before the order reduction is come into the approximation process. The denominator polynomial of the reduced order is obtained by the improved pole clustering technique while numerator polynomial of reduced order is determined through the pade approximation method. The reduced order model so obtained preserves the stability of the higher order system. The proposed method is validated by numerical examples from the literature.


 Improved Pole Clustering, Integral Square Error (ISE), Kharitonov theorem, Model Order Reduction, Pade Approximation


  1. Ahagnost, J. J., Desoer, C. A.  andMinnichelli, R. J. “An elementary proof of Kharitonov’s stability theory with extensions”, IEEE Trans. Auto. Control, Vol. 34, pp. 995-998, 1989.
  2. Ali Zilouchian and Dali Wang, “Model reduction of discrete linear systems via frequency domain balanced structure”, in Proc. Amer. Control Conference, Philadelphia, USA, Vol. 1, pp.162 – 166, 1998.
  3. Chang, C. Y., Chen, T. C. and Han, K. W. “Model Reduction using the stability-equation method and the Pade Approximation method”, J. Frank. Inst., Vol. 309, pp. 473-490, 1980.
  4. Fried land, B. and Hutton, M. F. “Routh approximations for reducing order of linear time- invariant systems”, IEEE Trans. on Auto. Control, Vol.20, pp. 329-337, 1975.
  5. Lucas, T. N. “Factor Division: A Useful Algorithm in Model Reduction”, IEE proc. Cont. The. Appl., Vol.130, No.6, pp. 362-364, 1983.
  6. Shamash, Y. “Continued Fraction Methods for the Reduction of Discrete Time Dynamic Systems”, Int. J. Cont. Sys., Vol. 20, pp. 267-275, 1974.
  7. Prasad, R. “Pade type model order reduction for multivariable systems using Routh-approximation”, Int. J. Comp. Elec. Engg., Vol.26, pp. 445-459, 2000.
  8. Bandyopadhyay, B., Gorez, R. and Ismail, O. “Discrete interval system reduction using Pade approximation to allow retention of dominant poles”,  IEEE Trans. on Cir. Sys., Vol. 44, No. 11, pp. 1075-1078, 1997.
  9. Dolgin, Y. and Zeheb, E. “On Routh-Pade model reduction of interval systems”, IEEE Trans. Auto. Cont., Vol. 48, No. 9, pp. 1610-1612, 2003.
  10. Ismail, O., Bandyopadhyay, B. and Gorez, R. “Discrete interval system reduction using Pade approximation to allow retention of dominant poles”, IEEE Trans. on Cir. Sys., Vol. 44, No. 11, pp. 1075-1078, 1997.
  11. Kranthikumar, D., Nagar, S. K. and Tiwari, J. P. “Model order reduction of Interval systems using Mihailov Criterion and Factor Division method”, Int. J. of Comp. Appl., Vol. 28, No.11, pp. 4-8, 2011.
  12. RajeswariMariappan, Certain Investigations on Model reduction and stability of Interval systems, Ph.D. thesis, Bharathiyar University, Coimbatore, 2004.
  13. Ramesh K., Nirmalkumar A. and Gurusamy G., “Order reduction of linear systems with an improved pole clustering”, Journal of Vibration and Control, Vol. 18, No. 12, pp. 1876-1885, 2012.
  14. Vishwakarma, C. B. and Prasad, R. “MIMO System Reduction Using Modified Pole Clustering and Genetic Algorithm”, Hind. Pub. Corp. Model.  Simu. Engg., Vol. 1, pp. 1-5, 2009.
  15. Pratheep, V.G, Dr. K. Venkatachalam, and Dr.K. Ramesh. “Model Order Reduction of Interval Systems by Pole Clustering Technique using GA.” journal of theoretical and applied information technology 66, no. 1 (2014).