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Finite-time \(H_\infty\) control of uncertain fractional-order neural networks. (English) Zbl 07195793
Summary: The problem of finite-time \(H_\infty\) control for uncertain fractional-order neural networks is investigated in this paper. Using finite-time stability theory and the Lyapunov-like function method, we first derive a new condition for problem of finite-time stabilization of the considered fractional-order neural networks via linear matrix inequalities (LMIs). Then a new sufficient stabilization condition is proposed to ensure that the resulting closed-loop system is not only finite-time bounded but also satisfies finite-time \(H_\infty\) performance. Three examples with simulations have been given to demonstrate the validity and correctness of the proposed methods.
MSC:
93D40 Finite-time stability
93B36 \(H^\infty\)-control
93C41 Control/observation systems with incomplete information
93B70 Networked control
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[1] Ali, Ms; Saravanan, S., Robust finite-time \(H_{\infty }\) control for a class of uncertain switched neural networks of neutral-type with distributed time varying delays, Neurocomputing, 177, 454-468 (2016)
[2] Ban, J.; Kwon, W.; Won, S.; Kim, S., Robust \(H_{\infty }\) finite-time control for discrete-time polytopic uncertain switched linear systems, Nonlinear Anal Hybrid Syst, 29, 348-362 (2018) · Zbl 1388.93035
[3] Baskar P, Padmanabhan S, Al MSi (2018) Finite-time \(H_{\infty }\) control for a class of Markovian jumping neural networks with distributed time varying delays-LMI approach. Acta Math Sci 38(2):561-579 · Zbl 1399.93051
[4] Boyd, S.; Ghaoui, Le; Feron, E.; Balakrishnan, V., Linear matrix inequalities in system and control theory (1994), Philadelphia: SIAM, Philadelphia · Zbl 0816.93004
[5] Chen L, Pan W, Wu RC, He YG (2015a) New result on finite-time stability of fractional-order nonlinear delayed systems. J Comput Nonlinear Dyn 10(6):064504
[6] Chen, Liping; Wu, Ranchao; Cao, Jinde; Liu, Jia-Bao, Stability and synchronization of memristor-based fractional-order delayed neural networks, Neural Networks, 71, 37-44 (2015) · Zbl 1398.34096
[7] Chen, L.; Liu, C.; Wu, R.; He, Y.; Chai, Y., Finite-time stability criteria for a class of fractional-order neural networks with delay, Neural Comput Appl, 27, 3, 549-556 (2016)
[8] Chen, L.; Huang, T.; Tenreiro Machado, Ja; Lopes, Am; Chai, Y.; Wu, Rc, Delay-dependent criterion for asymptotic stability of a class of fractional-order memristive neural networks with time-varying delays, Neural Netw, 118, 289-299 (2019)
[9] Cheng, J.; Zhu, H.; Zhong, S.; Zhang, Y.; Li, Y., Finite-time \(H_{\infty }\) control for a class of discrete-time Markovian jump systems with partly unknown time-varying transition probabilities subject to average dwell time switching, Int J Syst Sci, 46, 6, 1080-1093 (2015) · Zbl 1312.93109
[10] Dinh, X.; Cao, J.; Zhao, X.; Alsaadi, Fe, Finite-time stability of fractional-order complex-valued neural networks with time delays, Neural Process Lett, 46, 2, 561-580 (2017)
[11] Duarte-Mermoud, Ma; Aguila-Camacho, N.; Gallegos, Ja; Castro-Linares, R., Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems, Commun Nonlinear Sci Numer Simul, 22, 650-659 (2015) · Zbl 1333.34007
[12] Gahinet P, Nemirovskii A, Laub AJ, Chilali M (1995) LMI control toolbox for use with MATLAB. The MathWorks, Natick
[13] Guo, T.; Wu, B.; Wang, Ye; Wang, X., Delay-dependent robust finite-time \(H_{\infty }\) control for uncertain large delay systems based on a switching method, Circuits Syst Signal Process, 37, 11, 4753-4772 (2018)
[14] Kilbas, A.; Srivastava, H.; Trujillo, J., Theory and application of fractional diffrential equations (2006), New York: Elsevier, New York
[15] Li, S., LMI stability conditions and stabilization of fractional-order systems with polytopic and two-norm bounded uncertainties for fractional-order \(\alpha \): the \(1 < \alpha < 2\) case, Comput Appl Math, 37, 4, 5000-5012 (2018) · Zbl 1401.93165
[16] Li, C.; Deng, W., Remarks on fractional derivatives, Appl Math Comput, 187, 2, 777-784 (2007) · Zbl 1125.26009
[17] Lin, X.; Du, H.; Li, S., Finite-time boundedness and \(L_2-\) gain analysis for switched delay systems with norm-bounded disturbance, Appl Math Comput, 217, 5982-5993 (2014) · Zbl 1218.34082
[18] Liu, H.; Lin, X., Finite-time \(H_{\infty }\) control for a class of nonlinear system with time-varying delay, Neurocomputing, 149, 1481-1489 (2015)
[19] Ma, Yj; Wu, Bw; Wang, Ye, Finite-time stability and finite-time boundedness of fractional order linear systems, Neurocomputing, 173, 2076-2082 (2016)
[20] Pahnehkolaei, Seyed Mehdi Abedi; Alfi, Alireza; Machado, J. A. Tenreiro, Delay independent robust stability analysis of delayed fractional quaternion-valued leaky integrator echo state neural networks with QUAD condition, Applied Mathematics and Computation, 359, 278-293 (2019) · Zbl 1428.34020
[21] Pahnehkolaei, Seyed Mehdi Abedi; Alfi, Alireza; Machado, J. A. Tenreiro, Delay-dependent stability analysis of the QUAD vector field fractional order quaternion-valued memristive uncertain neutral type leaky integrator echo state neural networks, Neural Networks, 117, 307-327 (2019) · Zbl 1428.34020
[22] Peng, X.; Wu, H.; Cao, J., Global nonfragile synchronization in finite time for fractional-order discontinuous neural networks with nonlinear growth activations, IEEE Trans Neural Netw Learn Syst, 30, 7, 2123-2137 (2019)
[23] Rajivganthi, C.; Rihan, Fa; Lakshmanan, S.; Muthukumar, P., Finite-time stability analysis for fractional-order Cohen-Grossberg BAM neural networks with time delays, Neural Comput Appl, 29, 12, 1309-1320 (2018)
[24] Rakkiyappan, R.; Velmurugan, G.; Cao, J., Finite-time stability analysis of fractional-order complex-valued memristor-based neural networks with time delays, Nonlinear Dyn, 78, 4, 2823-2836 (2014) · Zbl 1331.34154
[25] Song, J.; He, S., Robust finite-time \(H_{\infty }\) control for one-sided Lipschitz nonlinear systems via state feedback and output feedback, J Frankl Inst, 352, 8, 3250-3266 (2015) · Zbl 1395.93128
[26] Thuan MV, Binh TN, Huong DC (2018) Finite-time guaranteed cost control of Caputo fractional-order neural networks. Asian J Control. 10.1002/asjc.1927
[27] Thuan, Mv; Huong, Dc; Hong, Dt, New results on robust finite-time passivity for fractional-order neural networks with uncertainties, Neural Process Lett, 50, 2, 1065-1078 (2019)
[28] Wang, S.; Shi, T.; Zhang, L.; Jasra, A.; Zeng, M., Extended finite-time \(H_{\infty }\) control for uncertain switched linear neutral systems with time-varying delays, Neurocomputing, 152, 377-387 (2015)
[29] Wang, L.; Song, Q.; Liu, Y.; Zhao, Z.; Alsaadi, Fe, Finite-time stability analysis of fractional-order complex-valued memristor-based neural networks with both leakage and time-varying delays, Neurocomputing, 245, 86-101 (2017)
[30] Wu, H.; Zhang, X.; Xue, S.; Wang, L.; Wang, Y., LMI conditions to global Mittag-Leffler stability of fractional-order neural networks with impulses, Neurocomputing, 193, 148-154 (2016)
[31] Xiang, W.; Xiao, J., \(H_{\infty }\) finite-time control for switched nonlinear discretetime systems with norm-bounded disturbance, J Franklin Inst, 348, 2, 331-352 (2011) · Zbl 1214.93043
[32] Xiang, Z.; Sun, Yn; Mahmoud, Ms, Robust finite-time \(H_{\infty }\) control for a class of uncertain switched neutral systems, Commun Nonlinear Sci Numer Simul, 17, 1766-1778 (2012) · Zbl 1239.93036
[33] Xie, Xc; Lam, J.; Li, Ps, Finite-time \(H_{\infty }\) control of periodic piecewise linear systems, Int J Syst Sci, 48, 11, 2333-2344 (2017) · Zbl 1372.93097
[34] Xu, C.; Li, P., On finite-time stability for fractional-order neural networks with proportional delays, Neural Process Lett, 50, 2, 1241-1256 (2019)
[35] Yang, X.; Song, Q.; Liu, Y.; Zhao, Z., Finite-time stability analysis of fractional-order neural networks with delay, Neurocomputing, 152, 19-26 (2015)
[36] Yang, Y.; He, Y.; Wang, Y.; Wu, M., Stability analysis of fractional-order neural networks: an LMI approach, Neurocomputing, 285, 82-93 (2018)
[37] Zhang, Shuo; Yu, Yongguang; Geng, Lingling, Stability Analysis of Fractional-Order Hopfield Neural Networks with Time-Varying External Inputs, Neural Processing Letters, 45, 1, 223-241 (2016)
[38] Zhang, Shuo; Yu, Yongguang; Yu, Junzhi, LMI Conditions for Global Stability of Fractional-Order Neural Networks, IEEE Transactions on Neural Networks and Learning Systems, 28, 10, 2423-2433 (2017)
[39] Zhang, H.; Ye, Y.; Cao, J.; Alsaedi, A., Delay-independent stability of Riemann-Liouville fractional neutral-type delayed neural networks, Neural Process Lett, 47, 2, 427-442 (2018)
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