Controllability results for singular switched system on time scales

Abstract

In this article, we introduced the time scale theory to study the controllability results of singular switched dynamic system. We evaluate the solution of slow-switched subsystem and fast-switched subsystem by using the mathematical induction. Also, we investigate the necessary and sufficient condition for controllability result of singular switched dynamic system followed by the state response of fast-switched and slow-switched subsystems. In the end, we gave an example that can show the efficacy of the proposed method.

Keywords:

• Controllability
• hybrid switched system
• pseudo-inverse
• singular switched system
• time scales

Acknowledgments

The authors would like to express their sincere thanks to the associate editor and anonymous reviewers for their constructive comments and suggestions to improve the quality of this manuscript. Also, the second author would like to thanks CSIR India for PhD research fellowship, file no: 09/1058(0025)/2021-EMR-I.

Disclosure statement

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

Additional information

Notes on contributors

Muslim Malik

Muslim Malik is Chairperson and Associate Professor of Mathematics at School of Mathematical and Statistical Sciences, Indian Institute of Technology Mandi, Himachal Pradesh, India. He received his PhD degree in Mathematics from Indian Institute of Technology Kanpur, Uttar Pradesh, India, in 2006. His research interests include time scale calculus, mathematical biology, inverse problems, switched systems, mathematical control theory, fractional, delay and neutral differential equations.

Bhim Kumar

Bhim Kumar was born in Uttar Pradesh, India, in 1996. He received the BSc (Hons.) degree in Mathematics from University of Delhi, India, in 2016 and MSc degree in Mathematics from Jamia Millia Islamia University, New Delhi, India, in 2019. He is currently pursuing his PhD degree in Applied Mathematics from School of Mathematical and Statistical Sciences, Indian Institute of Technology Mandi, Himachal Pradesh, India. His research interests include observability, controllability and stability analysis of switched systems on time scale calculus.