Stability of conformable fractional time-varying linear systems

Abstract

AbstractIn this paper, we investigate the exponential and asymptotic stability analysis of conformable fractional linear time-varying systems. We propose sufficient conditions for testing the asymptotic and exponential stability of conformable differential systems by using the notion of stable functions and differential Lyapunov inequalities. Furthermore, we apply the developed approach to the problem of conformable stabilisation and observer design for conformable fractional linear time-varying systems.Keywords: Conformable derivativeconformable time-varying systemsconformable exponential stabilityconformable asymptotic stabilityconformable observer Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationNotes on contributorsAbdellaziz BinidAbdellaziz Binid received his master degree from Sultan Moulay Slimane University in Applied Mathematics in 2014, the Ph.D. degree in control theory for distributed systems from Chouaib Doukkali University in 2020. He was a Visiting Postdoc at Qatar University, Doha, Qatar in 2023. His main research interest is in the area of system and control theory include infinite-dimensional system theory, observer design, positive systems, linear-quadratic optimal control, dynamical analysis and control of transport-reaction chemical processes and fractional systems.Toufik EnnouariToufik Ennouari received his master degree in control and dynamical systems from Chouaib Doukkali University in 2018, followed by a Ph.D. in control theory for distributed systems from the same university in 2023. His primary research focus lies within the field of system and control theory, encompassing topics such as infinite-dimensional system theory, controllability, observability, stability, positive systems, linear-quadratic optimal control, inverse optimal control, and conformable systems.Bouchra AbouzaidBouchra Abouzaid is a professor of mathematics at the National School of Applied Sciences, El-Jadida, Morocco. She received the DESA degree in mathematical engineering in 2003 and the Ph.D. degree on Applied Mathematics in 2008, both from Chouaib Doukkali University (Morocco). His research interests include dynamical system and control theory, especially distributed parameter (infinite-dimensional) system theory and applications.