An International Journal of Optimization and Control: Theories & Applications ISSN:2146-0957 eISSN:2146-5703 Vol.13, No.2, pp.259-268 (2023) http://doi.org/10.11121/ijocta.2023.1327 RESEARCH ARTICLE Some stability results on non-linear singular differential systems with random impulsive moments Arumugam Vinodkumar a* , Sivakumar Harinie a , Michal Feˇ ckan b,c Jehad Alzabut d,e a Department of Mathematics, Amrita School of Physical Sciences, Coimbatore-641 112, Amrita Vishwa Vidyapeetham, India b Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynsk´a dolina, 842 48, Bratislava, Slovakia c Mathematical Institute, Slovak Academy of Sciences, ˇ Stef´anikova 49, 814 73 Bratislava, Slovakia d Department of Mathematics and General Sciences, Prince Sultan University, 11586 Riyadh, Saudi Arabia e Department of Industrial Engineering, OST ˙ IM Technical University, Ankara 06374, Turkey a vinodkumar@cb.amrita.edu, hariniesiva960@gmail.com, Michal.Fecka@fmph.uniba.sk, jalzabut@psu.edu.sa ARTICLE INFO ABSTRACT Article History: Received 4 October 2022 Accepted 31 May 2023 Available 29 July 2023 This paper studies the exponential stability for random impulsive non-linear singular differential systems. We established some new sufficient conditions for the proposed singular differential system by using the Lyapunov function method with random impulsive time points. Further, to validate the theoret- ical results’ effectiveness, we finally gave two numerical examples that study with graphical illustration and an additional example involving matrices with complex entries, proving the results to be true in that case as well. Keywords: Random impulses Lyapunov function Exponential stability Singular differential systems AMS Classification 2010: 34A37; 34B16; 37B25 1. Introduction Singular systems are widely connected to various applications such as power systems, electrical net- works, and robotics. However, it has some ex- ceptional features like regular and impulse free that do not exist in normal state-space systems. These exceptional characteristics may cause some challenges upon studying the singular systems. Further, because of the singularity matrix E, it is not easy to formulate easy-to-check conditions for analysis and synthesis problems. Due to the above justifications, the study of singular sys- tems has been scrutinized more attention over the past decades [1]. The past two decades have spotted an important development on the the- ory of singular differential systems (SDSs), and many basic and most significant concepts have been favorably examined including stability anal- ysis, stabilization, guaranteed cost control, filter- ing, observer design, sliding mode control and so on [2, 3]. The main target is to show the lat- est developments in the analysis and synthesis of SDSs. Since the system is chronicled by algebraic and differential equations, the SDSs may disclose instability behavior and thus poor performance may be raised on the basis of presence of time delay. Hence the investigation of stability char- acter of SDSs becomes compulsory. By apply- ing various methods and ideas, several authors have studied the SDS. In [4], the author stud- ied the delay-dependent stability criteria by using Writinger-based inequality. The delay-dependent robust stability norms for two classes of SDSs with norm-bounded uncertainties are discussed in [5]. *Corresponding Author 259