International Journal of Mathematical, Engineering and Management Sciences

ISSN: 2455-7749

Dominant Pole Based Approximation for Discrete Time System

Department of Electrical Engineering, Madan Mohan Malaviya University of Technology, Gorakhpur, India.

Awadhesh Kumar
Department of Electrical Engineering, Madan Mohan Malaviya University of Technology, Gorakhpur, India.


Received on March 11, 2018
Accepted on November 03, 2018


This paper presents an effective procedure for model order reduction of discrete time control system. The exact model derived from complex dynamic systems proves to be very complicated for analysis, control and design. This necessity brings about using a tool known as model order reduction technique or model simplification. A novel mixed method has been implemented in this paper for reducing the order of the large scale dynamic discrete system. Dominant pole based pole clustering method has been used to derive the coefficients of denominator polynomial while Padé approximation has been applied to obtain the coefficients of numerator polynomial of the reduced order model. The proposed method is quite simple and able to generate a stable reduced order model from high order stable discrete systems. The dominancy of poles has been decided by values of the ratio of residue to its pole. The pole is considered dominant which have larger ratio value. An illustrative example has been considered to show the various reduction steps. The result obtained confirms the effectiveness of the approach.

Keywords- Dominant pole, Padé approximant, Pole clustering, Reduced order model, Residue based pole clustering.


Richa,& Kumar, A. (2019). Dominant Pole Based Approximation for Discrete Time System. International Journal of Mathematical, Engineering and Management Sciences, 4(1), 56-65.

Conflict of Interest

The authors confirm that there is no conflict of interest to declare for this publication.


The authors would like to thank reviewers for their constructive comments and for their valuable suggestions towards the improvement of the paper.


Bistritz, Y. U. V. A. L., & Shaked, U. (1984). Discrete multivariable system approximations by minimal Padé-type stable models. IEEE Transactions on Circuits and Systems, 31(4), 382-390.

Choo, Y. (2006). Suboptimal bilinear Routh approximant for discrete systems. Journal of Dynamic Systems, Measurement, and Control, 128(3), 742-745.

Gupta, M. K., & Kumar, A. (2016). Model reduction of continuous and discrete time systems using differentiation method with many clustering techniques. i-Manager's Journal on Instrumentation & Control Engineering, 4(3), 27.

Hutton, M., & Friedland, B. (1975). Routh approximations for reducing order of linear, time-invariant systems. IEEE Transactions on Automatic Control, 20(3), 329-337.

Kumar, A., & Chandra, D. (2014). Improved Padé-Pole clustering approximant. In International Conference on Computer Science and Electronics Engineering, pp. 28-32.

Mukherjee, S., & Mittal, R. C. (2005). Model order reduction using response-matching technique. Journal of the Franklin Institute, 342(5), 503-519.

Ramesh, K., Ganesan, R. G., & Mahalakshmi, K. (2017). Approximation and optimization of discrete systems using order reduction technique. Energy Procedia, 117, 761-768.

Sinha, A. K., & Pal, J. (1990). Simulation based reduced order modelling using a clustering technique. Computers & Electrical Engineering, 16(3), 159-169.

Singh, V., Chandra, D., & Kar, H. (2004). Improved Routh-Pade/spl acute/approximants: a computer-aided approach. IEEE Transactions on Automatic Control, 49(2), 292-296.

Shamash, Y. (1974). Stable reduced-order models using Padé-type approximations. IEEE Transactions on Automatic Control, 19(5), 615-616.

Singh, V. P., & Chandra, D. (2012). Model reduction of discrete interval system using clustering of poles. International Journal of Modelling, Identification and Control, 17(2), 116-123.

Takahashi, S., Yamanaka, K., & Yamada, M. (1987). Detection of dominant poles of systems with time delay by using Padé approximation. International Journal of Control, 45(1), 251-254.

Vishwakarma, C. B., & Prasad, R. (2008). System reduction using modified pole clustering and Pade approximation. XXXII National Systems Conference, NSC 2008, December 17-19, 2008.

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