Finite-time Stabilization of Delayed Uncertain Systems Using a Novel Integral Inequality Approach
| Authors | El H. Aouchicha1, Nabil El Fezazi2,3, , Mohamed Fahim4, Said Idrissi3,5, Ismail Lagrat6, Muhammad Iqbal Zakaria7, Amine El Fathi1, El Houssaine Tissir3 |
| Affiliations |
1LRSDI Laboratory, Faculty of Sciences and Techniques, Abdelmalek Essaâdi University, Al Hoceïma, Morocco 2IMD Team, Higher School of Technology of Dakhla, Ibn Zohr University, Agadir, Morocco 3LISAC Laboratory, Faculty of Sciences Dhar El Mehraz, Sidi Mohammed Ben Abdellah University, Fez, Morocco 4Computer Science Research Laboratory, Ibn Tofail University, Kenitra, Morocco 5LASTIMI Laboratory, Higher School of Technology of Sale, Mohammed V University, Rabat, Morocco 6Laboratory of Advanced Systems Engineering, National School of Applied Sciences, Ibn Tofail University, Keni-tra, Morocco 7School of Electrical Engineering, College of Engineering, Universiti Teknologi MARA, Shah Alam, Malaysia |
| Е-mail | houssinftouhi@gmail.com |
| Issue | Volume 17, Year 2025, Number 4 |
| Dates | Received 18 April 2025; revised manuscript received 22 August 2025; published online 29 August 2025 |
| Citation | El H. Aouchicha, Nabil El Fezazi, et al., J. Nano- Electron. Phys. 17 No 4, 04015 (2025) |
| DOI | https://doi.org/10.21272/jnep.17(4).04015 |
| PACS Number(s) | 07.05.Kf |
| Keywords | Finite-time stability (FTS), Uncertain systems, Free-matrix-based integral inequality (FMII). |
| Annotation |
Some new delay-dependent finite-time stability (FTS) conditions are provided and applied to the design problem of FT controllers. First, based on a new integral inequality and a simple Lyapunov-Krasovskii Functional (LKF), delay-dependent FTS criteria are proposed by introducing some free-weighting matrices. Thus, a new approximation of the unique integral that appears in the LKF derivative is proposed using an integral inequality, called free-matrix-based integral inequality (FMII). Then, memoryless and memory state-feedback controllers (MSC and MC) are designed to ensure FTS of delay-dependent uncertain systems, which are less conservative than others found in the literature. Although some results improve the stability criteria, FTS has received little attention, and more results can be attained to reduce the conservatism. That is the keystone of our research. The time-varying delays are bounded and differentiable with upper bound of delay derivatives. Also, the sufficient conditions obtained in this paper are established in terms of Linear Matrix Inequalities (LMIs) to achieve the desired performance. 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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