| Title:
|
Tighter settling-time bounds for fixed-time stable systems (English) |
| Author:
|
Chen, Jiale |
| Author:
|
Sun, Weigang |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
62 |
| Issue:
|
3 |
| Year:
|
2026 |
| Pages:
|
546-559 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper addresses the problem of refining settling-time upper-bound estimates for fixed-time stable systems under a three-term Lyapunov characterization. Without resorting to inequality-based techniques or special functions, a closed-form analytical upper bound for the settling-time function is derived using only elementary functions. Comparative analyses demonstrate that the proposed bound is tighter than existing results. The theoretical findings are further validated through the design of a fixed-time controller for a memristive neural network, with numerical simulations confirming the accuracy of the estimated settling time and the independence of the control scheme from initial conditions. (English) |
| Keyword:
|
fixed-time stability |
| Keyword:
|
settling-time estimation |
| Keyword:
|
Lyapunov inequality |
| Keyword:
|
nonlinear systems |
| Keyword:
|
generalized homogeneity |
| MSC:
|
93C10 |
| MSC:
|
93D05 |
| MSC:
|
93D40 |
| DOI:
|
10.14736/kyb-2026-3-0546 |
| . |
| Date available:
|
2026-07-15T16:29:50Z |
| Last updated:
|
2026-07-15 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153687 |
| . |
| Reference:
|
[1] Aldana-López, R., Gómez-Gutiérrez, D., Jiménez-Rodríguez, E., Sánchez-Torres, J. D., Defoort, M.: Enhancing the settling time estimation of a class of fixed-time stable systems..Int. J. Robust Nonlinear Control 29 (2019), 4135-4148. |
| Reference:
|
[2] Bhat, S. P., Bernstein, D. S.: Finite-time stability of continuous autonomous systems..SIAM J. Control Optim. 38 (2000), 751-766. Zbl 0945.34039, |
| Reference:
|
[3] Cai, Z., Huang, L., Wang, Z.: Fixed-time control and estimation of discontinuous fuzzy neural networks: novel Lyapunov method of fixed-time stability..IEEE Trans. Neural Netw. Learn. Syst. 35 (2024), 16616-16629. |
| Reference:
|
[4] Chen, C., Li, L., Peng, H., Yang, Y., Mi, L., Zhao, H.: A new fixed-time stability theorem and its application to the fixed-time synchronization of neural networks..Neural Netw. 123 (2020), 412-419. |
| Reference:
|
[5] Feng, L., Hu, C., Yu, J., Jiang, H., Wen, S.: Fixed-time synchronization of coupled memristive complex-valued neural networks..Chaos Solit. Fractals 148 (2021), 110993. |
| Reference:
|
[6] Gao, G., Ge, H., Wang, G., Wang, L.: Preassigned-time sliding-mode control of chaotic memristive neural networks with time-varying delays..IEEE Trans. Circuits Syst. II, Exp. Briefs 72 (2025), 823-827. |
| Reference:
|
[7] Giap, V. N., Nguyen, Q. D., Trung, N. K., Huang, S.-C.: Time-varying disturbance observer based on sliding-mode observer and double phases fixed-time sliding mode control for a TS fuzzy micro-electro-mechanical system gyroscope..J. Vib. Control 29 (2023), 1927-1942. |
| Reference:
|
[8] Guo, C., Hu, J.: Fixed-time stabilization of high-order uncertain nonlinear systems: Output feedback control design and settling time analysis..J. Syst. Sci. Complex. 36 (2023), 1351-1372. |
| Reference:
|
[9] Hosseinabadi, P. A., Ahmed, S., Pota, H., Mekhilef, S., Konstantinou, G., Negnevitsky, M., Hassan, W.: FPPT and fixed-time sliding mode controller for single-stage grid-integrated PV systems..IEEE Trans. Ind. Appl. 61 (2025), 8357-8372. |
| Reference:
|
[10] Hu, C., Jiang, H.: Special functions-based fixed-time estimation and stabilization for dynamic systems..IEEE Trans. Syst. Man Cybern. Syst. 52 (2022), 3251-3262. |
| Reference:
|
[11] Hu, C., Yu, J., Chen, Z., Jiang, H., Huang, T.: Fixed-time stability of dynamical systems and fixed-time synchronization of coupled discontinuous neural networks..Neural Netw. 89 (2017), 74-83. |
| Reference:
|
[12] Hu, C., He, H., Jiang, H.: Fixed/preassigned-time synchronization of complex networks via improving fixed-time stability..IEEE Trans. Cybern. 51 (2021), 2882-2892. |
| Reference:
|
[13] Kong, F., Zhu, Q., Huang, T.: New fixed-time stability lemmas and applications to the discontinuous fuzzy inertial neural networks..IEEE Trans. Fuzzy Syst. 29 (2021), 3711-3722. |
| Reference:
|
[14] Li, D., Li, H., Hu, C., Jiang, H., Cao, J.: Quasi-projective synchronization of discrete-time fractional-order delayed memristive neural networks with uncertainties..IEEE Trans. Cybern. 56 (2026), 414-426. |
| Reference:
|
[15] Mapui, A., Jamal, M. A., Mukhopadhyay, S.: On optimal upper bound for the settling time of fixed-time stable systems and its application in secure communication..Nonlinear Dyn. 113 (2025), 5359-5381. |
| Reference:
|
[16] Ou, M., Sun, H., Zhang, Z., Li, L., Wang, X.: Fixed-time tracking control for nonholonomic mobile robot..Kybernetika 57 (2021), 220-235. |
| Reference:
|
[17] Mishra, J., Patel, R., Yu, X., Jalili, M.: Recursive surface structure for fixed-time convergence with applications to power systems..IET Control Theory Appl. 12 (2018), 2595-2604. |
| Reference:
|
[18] Moulay, E., Léchappé, V., Bernuau, E., Plestan, F.: Robust fixed-time stability: application to sliding-mode control..IEEE Trans. Autom. Control 67 (2022), 1061-1066. |
| Reference:
|
[19] Parsegov, S., Polyakov, A., Shcherbakov, P.: Nonlinear fixed-time control protocol for uniform allocation of agents on a segment..Proc. IEEE Conf. Decision Control (2012), 7732-7737. |
| Reference:
|
[20] Polyakov, A.: Nonlinear feedback design for fixed-time stabilization of linear control systems..IEEE Trans. Autom. Control 57 (2012), 2106-2110. |
| Reference:
|
[21] Polyakov, A.: Generalized Homogeneity in Systems and Control. Volume I..Springer, 2025. |
| Reference:
|
[22] Song, Z., Li, P.: Fixed-time adaptive command-filter-based event-triggered control of constrained switched nonlinear systems with unmodeled dynamics..Kybernetika 61 (2025), 32-57. |
| Reference:
|
[23] Sun, W., Guo, W., Li, B., Wen, S., Cao, J., Abdel-Aty, M.: Finite/fixed-time controls of neural networks in a signed graph..IEEE Trans. Syst. Man Cybern. Syst. 54 (2024), 1049-1058. |
| Reference:
|
[24] Wang, L., Jiang, S., Ge, M., Hu, C., Hu, J.: Finite-/fixed-time synchronization of memristor chaotic systems and image encryption application..IEEE Trans. Circuits Syst. I, Reg. Papers 68 (2021), 4957-4969. |
| Reference:
|
[25] Wang, L., Zeng, Z., Ge, M.: A disturbance rejection framework for finite-time and fixed-time stabilization of delayed memristive neural networks..IEEE Trans. Syst. Man Cybern. Syst. 51 (2021), 905-915. |
| Reference:
|
[26] Wang, X., Pan, L., Tian, Y., Liu, Y., Li, L.: Adaptive fault-tolerant fixed-time sliding mode tracking control for steer-by-wire system with dual-three-phase PMSM..IEEE Trans. Veh. Technol. 74 (2025), 7554-7564. |
| Reference:
|
[27] Zhang, X., Shi, R.: A novel fixed-time stability theorem and its application to nonlinear manipulator trajectory tracking control..Int. J. Robust Nonlinear Control 35 (2025), 4712-4723. |
| Reference:
|
[28] Zhang, Y., Lin, P., Chen, J., Sun, W.: A hybrid cryptosystem for medical image security: integrating finite fields with conservative hyperchaos..Nonlinear Dyn. 114 (2026), 129. |
| Reference:
|
[29] Zuo, Z., Tie, L.: Distributed robust finite-time nonlinear consensus protocols for multi-agent systems..Int. J. Syst. Sci. 47 (2016), 1366-1375. |
| . |
