Properties of the stability boundary in linear distributed-order systems

ABSTRACT

This paper mainly focuses on some behaviours of the bounded input-bounded output (BIBO) stability boundary in the linear distributed-order system (LDOS). Finding an association between changes of weight functions of LDOS and variation of its BIBO stability boundary is the other aim of this paper. To achieve these goals, the tangential lines of the BIBO stability boundary for the extremely high and low frequencies are founded in the first step. Then, the additive identity and the multiplicative identity for the weight function maintaining the stability boundary intact are determined. In addition, it is proved that multiplying a set of multiplication factors in the form of polynomials to the weight functions would guarantee the increment of the stability region. To validate the presented results, comparisons among the stability boundary of several different LDOS are performed. Simulation outcomes are in agreement with the extracted results.

KEYWORDS:

• Stability boundary analysis
• distributed-order system
• BIBO stability

Acknowledgements

This work was supported by the Iran National Science Foundation (INSF).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Ehsan Majma

Ehsan Majma is an M.Sc graduated student in electrical engineering department of Sharif University of Technology, Tehran. His research area is focused on the analysis of behaviour of stability boundary of linear distributed-order systems. He is currently working as a Lecturer and Laboratory Instructor at Samaparan Aviation Training Centre, Tehran, Iran.

Mohammad Saleh Tavazoei

Mohammad Saleh Tavazoei received the B.Sc., M.Sc. and Ph.D. degrees in electrical engineering from the Sharif University of Technology, Tehran, Iran, in 2003, 2005 and 2008, respectively. He is currently an Associate Professor with the Department of Electrical Engineering, Sharif University of Technology. His current research interests include fractional-order circuits and systems and their applications in engineering. He was a recipient of the Young Investigator Award of the IEEE Iran Section in 2012. He was also selected as the Prominent Young Scientist in electrical and computer engineering by the Academy of Sciences of Iran in 2017.