Model Order Reduction of LTI Interval Systems Using Differentiation Method Based on Kharitonov’s Theorem

Abstract

A new reduction method is proposed to reduce the higher order interval system. The proposed reduced-order interval model is achieved based on the differentiation method using the Kharitonov’s theorem. This method is significant for both single-input single-output interval systems and multi-input multi-output interval systems. This method is simple in mathematical calculation and preserves the dominant characteristics of the original interval system in its reduced-order interval models. The suggested method provides stable reduced-order models if the original system is stable. To show the effectiveness of this technique, it is illustrated with benchmark problems. The results show the close approximation of the reduced-order model obtained by the proposed technique with the original system. Furthermore, the performance of the suggested technique validated qualitatively in terms of time response specifications and performance indices by comparing with other well-known reduction methods. These results exhibit the effectiveness and efficiency of the proposed technique. Moreover, this method also extended for discrete-time interval systems.

KEYWORDS:

• Differentiation method
• Integral square error
• Interval systems
• Kharitonov’s theorem
• Model order reduction
• Sixteen plant theorem
• Time response specifications

Additional information

Notes on contributors

Sudharsana Rao Potturu

P Sudharsana Rao was born in Guntur, Andhra Pradesh, India, in 1988. He received his BTech in electronics and instrumentation engineering from JNTU Kakinada, Andhra Pradesh, India, in 2010, and MTech in electrical engineering with control system engineering specialization from Indian Institute of Technology Kharagpur, West Bengal, India, in 2013. Currently, he is pursuing PhD at Department of Electrical Engineering, Indian Institute of Technology Roorkee, Uttarakhand, India. His area of interest includes biomedical engineering, control systems, model order reduction, interval systems and controller design. Corresponding author. Email: [email protected]

Rajendra Prasad

Rajendra Prasad was born in Hangawali (Saharanpur), India, in 1953. He received BSc (Hons.) from Meerut University, India, in 1973. He received BE, ME, and PhD degrees in electrical engineering from the University of Roorkee, India, in 1977, 1979, and 1990, respectively. He served as a lecturer in Electrical Engineering Department, University of Roorkee, India, from 1983 to 1996. He worked as an assistant professor from 1996 to 2001 and associate professor from 2001 to 2009. Presently, he is a professor in the Department of Electrical Engineering, Indian Institute of Technology Roorkee, India. He has published around 300 papers in various journals/conferences and received 15 awards. He has guided 16 PhDs, and presently, four PhDs are under progress. His main research interests include model order reduction, data analysis, controller design, and optimization techniques. Email: [email protected]