Finite-time Stabilization of Discrete-time Linear Systems Subject to Time-varying Delay Using a Novel Summation Inequality
| Authors | Nabil El Fezazi1,2, Mohamed Fahim3, Said Idrissi2,4, El Houssine Aouchicha5, Ismail Lagrat6 , Muhammad Iqbal Zakaria7 , El Houssaine Tissir2, Mo’tassem Al-Arydah8 |
| Affiliations |
1IMD Team, Higher School of Technology of Dakhla, Ibn Zohr University, Agadir, Morocco 2LISAC Laboratory, Faculty of Sciences Dhar El Mehraz, Sidi Mohammed Ben Abdellah University, Fez, Morocco 3Computer Science Research Laboratory, Ibn Tofail University, Kenitra, Morocco 4LASTIMI Laboratory, Higher School of Technology of Sale, Mohammed V University, Rabat, Morocco 5LRSDI Laboratory, Faculty of Sciences and Techniques, Abdelmalek Essaâdi University, Al Hoceïma, Morocco 6Laboratory of Advanced Systems Engineering, National School of Applied Sciences, Ibn Tofail University, Kenitra, Morocco 7School of Electrical Engineering, College of Engineering, Universiti Teknologi MARA, Shah Alam, Malaysia 8Department of Mathematics, Khalifa University, Abu Dhabi P.O. Box 127788, United Arab Emirates |
| Е-mail | n.elfezazi@uiz.ac.ma |
| Issue | Volume 17, Year 2025, Number 5 |
| Dates | Received 10 August 2025; revised manuscript received 22 October 2025; published online 30 October 2025 |
| Citation | Nabil El Fezazi, Mohamed Fahim, et al., J. Nano- Electron. Phys. 17 No 5, 05028 (2025) |
| DOI | https://doi.org/10.21272/jnep.17(5).05028 |
| PACS Number(s) | 07.05.Tp |
| Keywords | Finite-time stability (FTS), Discrete-time systems, Free-Matrix-Based-Integral (FMBI). |
| Annotation |
To improve the performance and reduce the conservatism of developed results over a FT (finite-time) interval, a new analysis and design technique is proposed in this paper. Then, a system is said to be FT stable if, at a certain time interval, its state does not exceed some bounds. Hence, novel delay-dependent finite-time stability (FTS) conditions are provided for discrete-time linear systems subject to time-varying delay. The delay-dependent stability criteria, which take into account the information on the size of time delays, are less conservative than delay-independent ones. Then, the obtained conditions are applied to the design problem of FT controllers. For this reason, a new approximation of the single summation that appears in the Lyapunov-Krasovskii functional (LKF) is studied using an innovative Free-Matrix-Based-Integral (FMBI) inequality. This has led to the proposal of new conditions in the form of LMIs that ensure FTS. Although some results improve the stability criteria, FTS has received little attention, and more results can be obtained to reduce the conservatism. That is the keystone of our research. To illustrate the potential gain of employing this new approach, a detailed numerical example is provided. Finally, a less conservative LMI-based design is proposed and solved with MATLAB showing very good results. |
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List of References |
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