Abstract
This article is devoted to resolving the issue of time-varying fault in the fractional-order financial system subject to constant delay. A fault-tolerant control is addressed to solve the faults which occur by unpredictable affairs in the financial system. Further, a set of adequate constraints in the form of Linear Matrix Inequalities are derived to ensure asymptotic stability of the considered system under the theorem of Lyapunov. More precisely, Lyapunov–Krasovskii candidates are employed independently with various state-space trajectories such as interest rate, investment demand and price index. Lastly, a numerical example is provided to support the constructed theoretical results.
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References
Tacha OI, Volos CK, Kyprianidis IM, Stouboulos IN, Vaidyanathan S, Pham VT (2016) Analysis, adaptive control and circuit simulation of a novel nonlinear finance system. Appl Math Comput 276:200–217
Vaidyanathan S, Volos CK, Tacha OI, Kyprianidis IM, Stouboulos IN, Pham VT (2016) Analysis, control and circuit simulation of a novel 3-D finance chaotic system. Adv Appl Chaotic Syst 636:495–512
Hajipour A, Tavakoli H (2017) Dynamic analysis and adaptive sliding mode controller for a chaotic fractional incommensurate order financial system. Int J Bifurc Chaos 27(13):1750198
Hajipour A, Hajipour M, Baleanu D (2018) On the adaptive sliding mode controller for a hyperchaotic fractional-order financial system. Phys A 497:139–153
Camacho NA, Mermoud MAD, Gallegos JA (2014) Lyapunov functions for fractional order systems. Commun Nonlinear Sci Numer Simul 19(9):2951–2957
Boroujeni EA, Momeni HR (2012) Observer based control of a class of nonlinear fractional order systems using LMI. Int J Sci Eng Investig 1(1):48–52
Zhang ES, Yu Y, Yu J (2017) LMI conditions for global stability of fractional-order neural networks. IEEE Trans Neural Netw Learn Syst 28(10):2423–2433
Li H, Li S, Lia G, Wang H (2017) Robust adaptive control for fractional-order financial chaotic systems with system uncertainties and external disturbances. J Inf Technol Control 46(2):246–259
Zhang Z, Zhang J, Cheng F, Xu Y (2019) Bifurcation analysis and stability criterion for the nonlinear fractional-order three-dimensional financial system with delay. Asian J Control 21(6):1–11
Huang C, Cao J (2017) Active control strategy for synchronization and anti-synchronization of a fractional chaotic financial system. Phys A 473:262–275
Dhanalakshmi P, Senpagam S, Mohanapriya R (2019) Robust fault estimation controller for fractional-order delayed system using quantized measurement. Int J Dyn Control. https://doi.org/10.1007/s40435-019-00549-2
You F, Li H, Wang F, Guan S, Zhang K (2015) Robust fast adaptive fault estimation for systems with time-varying interval delay. J Frankl Inst 352:5486–5513
You F, Li H, Wang F, Guan S, Zhang K (2015) Fractional-order adaptive fault estimation for a class of nonlinear fractional-order systems. In: 2015 American control conference (ACC). Chicago, IL, pp 3804–3809
Han J, Zhang H, Wang Y, Zhang K (2018) Fault estimation and fault-tolerant control for switched fuzzy stochastic systems. IEEE Trans Fuzzy Syst 26(5):2993–3003
Li X, Ahn CK, Lu D, Guo S (2019) Robust simultaneous fault estimation and nonfragile output feedback fault-tolerant control for markovian jump systems. IEEE Trans Syst Man Cybern Syst 49(9):1769–1776
Vara RC, Novais P, Gil AB, Prieto J, Corchado JM (2019) Distributed continuous-time fault estimation control for multiple devices in IoT networks. IEEE Access 7:11972–11984
Zhang H, Ye R, Cao J, Alsaedi A (2018) Delay-independent stability of Riemann–Liouville fractional neutral-type delayed neural networks. Neural Process Lett 42:427–442
Li Y, Chen YQ, Podlubny I (2010) Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag–Leffler stability. Comput Math Appl 59:1810–1821
Acknowledgements
This research work of S. Senpagam is financially supported by Department of Science and Technology(DST)-Promotion of University Research and Scientific Excellence(PURSE) Phase-II, Government of India, New Delhi.
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Senpagam, S., Dhanalakshmi, P. & Mohanapriya, R. Fault estimation observer design for fractional-order financial system subject to time-delay. Int. J. Dynam. Control 9, 190–198 (2021). https://doi.org/10.1007/s40435-020-00642-x
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DOI: https://doi.org/10.1007/s40435-020-00642-x