Delay-dependent robust stability analysis of uncertain fractional-order neutral systems with distributed delays and nonlinear perturbations subject to input saturation

References

[1] Q. Wu, Q. Song, B. Hu, Z. Zhao, Y. Liu, and F. E. Alsaadi, “Robust stability of uncertain fractional order singular systems with neutral and time-varying delays,” Neurocomputing, vol. 411, no. 11, pp. 145–152, 2020. https://doi.org/10.1016/j.neucom.2020.03.015.Search in Google Scholar

[2] S. Arik, “New criteria for stability of neutral-type neural networks with multiple time delays,” IEEE Trans. Neural Network Learn. Syst., vol. 31, no. 5, pp. 1504–1513, 2019. https://doi.org/10.1109/TNNLS.2019.2920672.Search in Google Scholar PubMed

[3] T. Wang, T. Li, G. Zhang, and S. Fei, “Further triple integral approach to mixed-delay-dependent stability of time-delay neutral systems,” ISA (Instrum. Soc. Am.) Trans., vol. 70, pp. 116–124, 2017. https://doi.org/10.1016/j.isatra.2017.05.010.Search in Google Scholar PubMed

[4] J. Grzybowski, E. Macau, and T. Yoneyama, “The Lyapunov–Krasovskii theorem and a sufficient criterion for local stability of isochronal synchronization in networks of delay-coupled oscillators,” Phys. Nonlinear Phenom., vol. 346, pp. 28–36, 2017. https://doi.org/10.1016/j.physd.2017.01.005.Search in Google Scholar

[5] A. Elahi and A. Alfi, “Stochastic H∞ finite-time control of networked cascade control systems under limited channels, network delays and packet dropouts,” ISA (Instrum. Soc. Am.) Trans., vol. 97, pp. 352–364, 2020. https://doi.org/10.1016/j.isatra.2019.07.020.Search in Google Scholar PubMed

[6] K. Cui, J. Lu, C. Li, Z. He, and Y.-M. Chu, “Almost sure synchronization criteria of neutral-type neural networks with Lévy noise and sampled-data loss via event-triggered control,” Neurocomputing, vol. 325, pp. 113–120, 2019. https://doi.org/10.1016/j.neucom.2018.10.013.Search in Google Scholar

[7] Q.-L. Han, “Stability analysis for a partial element equivalent circuit (PEEC) model of neutral type,” Int. J. Circ. Theor. Appl., vol. 33, no. 4, pp. 321–332, 2005. https://doi.org/10.1002/cta.323.Search in Google Scholar

[8] M. Barbarossa, K. Hadeler, and C. Kuttler, “State-dependent neutral delay equations from population dynamics,” J. Math. Biol., vol. 69, no. 4, pp. 1027–1056, 2014. https://doi.org/10.1007/s00285-014-0821-8.Search in Google Scholar PubMed

[9] F. Du and J.-G. Lu, “Finite-time stability of neutral fractional order time delay systems with Lipschitz nonlinearities,” Appl. Math. Comput., vol. 375, p. 125079, 2020. https://doi.org/10.1016/j.amc.2020.125079.Search in Google Scholar

[10] W. Chen, S. Xu, Y. Li, and Z. Zhang, “Stability analysis of neutral systems with mixed interval time-varying delays and nonlinear disturbances,” J. Franklin Inst., vol. 357, no. 6, pp. 3721–3740, 2020. https://doi.org/10.1016/j.jfranklin.2020.02.038.Search in Google Scholar

[11] Y. He, M. Wu, J.-H. She, and G.-P. Liu, “Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays,” Syst. Contr. Lett., vol. 51, no. 1, pp. 57–65, 2004. https://doi.org/10.1016/s0167-6911(03)00207-x.Search in Google Scholar

[12] F. Zheng and P. M. Frank, “Robust control of uncertain distributed delay systems with application to the stabilization of combustion in rocket motor chambers,” Automatica, vol. 38, no. 3, pp. 487–497, 2002. https://doi.org/10.1016/s0005-1098(01)00232-1.Search in Google Scholar

[13] E. Kaslik and M. Neamţu, “Dynamics of a tourism sustainability model with distributed delay,” Chaos, Solit. Fractals, vol. 133, p. 109610, 2020. https://doi.org/10.1016/j.chaos.2020.109610.Search in Google Scholar

[14] B. Niu and Y. Guo, “Bifurcation analysis on the globally coupled Kuramoto oscillators with distributed time delays,” Phys. Nonlinear Phenom., vol. 266, pp. 23–33, 2014. https://doi.org/10.1016/j.physd.2013.10.003.Search in Google Scholar

[15] M. Sardar, S. Biswas, and S. Khajanchi, “The impact of distributed time delay in a tumor-immune interaction system,” Chaos, Solit. Fractals, vol. 142, p. 110483, 2021. https://doi.org/10.1016/j.chaos.2020.110483.Search in Google Scholar

[16] R. Roopnarain and S. R. Choudhury, “Amplitude death, oscillation death, and periodic regimes in dynamically coupled Landau–Stuart oscillators with and without distributed delay,” Math. Comput. Simulat., vol. 187, pp. 30–50, 2021. https://doi.org/10.1016/j.matcom.2021.02.006.Search in Google Scholar

[17] Y. Chen, W. Qian, and S. Fei, “Improved robust stability conditions for uncertain neutral systems with discrete and distributed delays,” J. Franklin Inst., vol. 352, no. 7, pp. 2634–2645, 2015. https://doi.org/10.1016/j.jfranklin.2015.03.040.Search in Google Scholar

[18] H. Zhang, R. Ye, S. Liu, J. Cao, A. Alsaedi, and X. Li, “LMI-based approach to stability analysis for fractional-order neural networks with discrete and distributed delays,” Int. J. Syst. Sci., vol. 49, no. 3, pp. 537–545, 2018. https://doi.org/10.1080/00207721.2017.1412534.Search in Google Scholar

[19] P.-L. Liu, “Improved delay-dependent stability of neutral type neural networks with distributed delays,” ISA (Instrum. Soc. Am.) Trans., vol. 52, no. 6, pp. 717–724, 2013. https://doi.org/10.1016/j.isatra.2013.06.012.Search in Google Scholar PubMed

[20] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204, Amsterdam, Elsevier, 2006.10.1016/S0304-0208(06)80001-0Search in Google Scholar

[21] D. Baleanu, S. S. Sajjadi, A. Jajarmi, and J. H. Asad, “New features of the fractional Euler–Lagrange equations for a physical system within non-singular derivative operator,” Eur. Phys. J. Plus, vol. 134, no. 4, p. 181, 2019. https://doi.org/10.1140/epjp/i2019-12561-x.Search in Google Scholar

[22] H.-Y. Yang, Y. Yang, F. Han, M. Zhao, and L. Guo, “Containment control of heterogeneous fractional-order multi-agent systems,” J. Franklin Inst., vol. 356, no. 2, pp. 752–765, 2019. https://doi.org/10.1016/j.jfranklin.2017.09.034.Search in Google Scholar

[23] B. Xiao, J. Luo, X. Bi, W. Li, and B. Chen, “Fractional discrete Tchebyshev moments and their applications in image encryption and watermarking,” Inf. Sci., vol. 516, pp. 545–559, 2020. https://doi.org/10.1016/j.ins.2019.12.044.Search in Google Scholar

[24] C. Zou, L. Zhang, X. Hu, Z. Wang, T. Wik, and M. Pecht, “A review of fractional-order techniques applied to lithium-ion batteries, lead-acid batteries, and supercapacitors,” J. Power Sources, vol. 390, pp. 286–296, 2018. https://doi.org/10.1016/j.jpowsour.2018.04.033.Search in Google Scholar

[25] K. M. Owolabi, “High-dimensional spatial patterns in fractional reaction–diffusion system arising in biology,” Chaos, Solit. Fractals, vol. 134, p. 109723, 2020. https://doi.org/10.1016/j.chaos.2020.109723.Search in Google Scholar

[26] N. H. Sau, D. T. Hong, B. V. Huyen, Huong, and M. V. Thuan, “Delay-dependent and order-dependent control for fractional-order neural networks with time-varying delay,” Differ. Equ. Dyn. Syst., pp. 1–15, 2021. https://doi.org/10.1007/s12591-020-00559-z.Search in Google Scholar

[27] V. Phat, P. Niamsup, and M. V. Thuan, “A new design method for observer-based control of nonlinear fractional-order systems with time-variable delay,” Eur. J. Contr., vol. 56, pp. 124–131, 2020. https://doi.org/10.1016/j.ejcon.2020.02.005.Search in Google Scholar

[28] S. M. A. Pahnehkolaei, A. Alfi, and J. T. Machado, “Uniform stability of fractional order leaky integrator echo state neural network with multiple time delays,” Inf. Sci., vol. 418, pp. 703–716, 2017. https://doi.org/10.1016/j.ins.2017.08.046.Search in Google Scholar

[29] N. H. Sau, M. V. Thuan, and N. T. T. Huyen, “Passivity analysis of fractional-order neural networks with time-varying delay based on LMI approach,” Circ. Syst. Signal Process., vol. 39, pp. 5906–5925, 2020. https://doi.org/10.1007/s00034-020-01450-6.Search in Google Scholar

[30] R. Rakkiyappan, G. Velmurugan, and J. Cao, “Finite-time stability analysis of fractional-order complex-valued memristor-based neural networks with time delays,” Nonlinear Dynam., vol. 78, no. 4, pp. 2823–2836, 2014. https://doi.org/10.1007/s11071-014-1628-2.Search in Google Scholar

[31] M. V. Thuan, T. N. Binh, and D. C. Huong, “Finite-time guaranteed cost control of caputo fractional-order neural networks,” Asian J. Contr., vol. 22, no. 2, pp. 696–705, 2020. https://doi.org/10.1002/asjc.1927.Search in Google Scholar

[32] J. Xiao, J. Cao, J. Cheng, S. Zhong, and S. Wen, “Novel methods to finite-time Mittag–Leffler synchronization problem of fractional-order quaternion-valued neural networks,” Inf. Sci., vol. 526, pp. 211–244, 2020.10.1016/j.ins.2020.03.101Search in Google Scholar

[33] P. Li, L. Chen, R. Wu, J. T. Machado, A. M. Lopes, and L. Yuan, “Robust asymptotic stability of interval fractional-order nonlinear systems with time-delay,” J. Franklin Inst., vol. 355, no. 15, pp. 7749–7763, 2018. https://doi.org/10.1016/j.jfranklin.2018.08.017.Search in Google Scholar

[34] D. C. Huong and M. V. Thuan, “Mixed H∞ and passive control for fractional nonlinear systems via LMI approach,” Acta Appl. Math., vol. 170, no. 1, pp. 37–52, 2020. https://doi.org/10.1007/s10440-020-00323-z.Search in Google Scholar

[35] M. V. Thuan, N. H. Sau, and N. T. T. Huyen, “Finite-time H∞ control of uncertain fractional-order neural networks,” Comput. Appl. Math., vol. 39, no. 2, pp. 1–19, 2020. https://doi.org/10.1007/s40314-020-1069-0.Search in Google Scholar

[36] K. Liu, J. Wang, Y. Zhou, and D. O’Regan, “Hyers–Ulam stability and existence of solutions for fractional differential equations with Mittag–Leffler kernel,” Chaos, Solit. Fractals, vol. 132, p. 109534, 2020. https://doi.org/10.1016/j.chaos.2019.109534.Search in Google Scholar

[37] M. V. Thuan, N. H. Sau, and N. T. T. Huyen, “New results on robust finite-time passivity for fractional-order neural networks with uncertainties,” Comput. Appl. Math., vol. 39, no. 59, pp. 1–18, 2020. https://doi.org/10.1007/s40314-020-1069-0.Search in Google Scholar

[38] J. Cheng, H. Zhu, S. Zhong, and G. Li, “Novel delay-dependent robust stability criteria for neutral systems with mixed time-varying delays and nonlinear perturbations,” Appl. Math. Comput., vol. 219, no. 14, pp. 7741–7753, 2013. https://doi.org/10.1016/j.amc.2013.01.062.Search in Google Scholar

[39] X. Zhang and Y. Chen, “Admissibility and robust stabilization of continuous linear singular fractional order systems with the fractional order α: the 0 < α < 1 case,” ISA (Instrum. Soc. Am.) Trans., vol. 82, pp. 42–50, 2018. https://doi.org/10.1016/j.isatra.2017.03.008.Search in Google Scholar PubMed

[40] P. Badri and M. Sojoodi, “Robust stabilisation of fractional-order interval systems via dynamic output feedback: an LMI approach,” Int. J. Syst. Sci., vol. 50, no. 9, pp. 1718–1730, 2019. https://doi.org/10.1080/00207721.2019.1622817.Search in Google Scholar

[41] R. Mohsenipour and M. F. Jegarkandi, “Robust stability analysis of fractional-order interval systems with multiple time delays,” Int. J. Robust Nonlinear Control, vol. 29, no. 6, pp. 1823–1839, 2019. https://doi.org/10.1002/rnc.4461.Search in Google Scholar

[42] M. V. Thuan, D. C. Huong, and D. T. Hong, “New results on robust finite-time passivity for fractional-order neural networks with uncertainties,” Neural Process. Lett., vol. 50, no. 2, pp. 1065–1078, 2019. https://doi.org/10.1007/s11063-018-9902-9.Search in Google Scholar

[43] M. V. Thuan and D. C. Huong, “Robust guaranteed cost control for time-delay fractional-order neural networks systems,” Optim. Contr. Appl. Methods, vol. 40, no. 4, pp. 613–625, 2019. https://doi.org/10.1002/oca.2497.Search in Google Scholar

[44] S. M. A. Pahnehkolaei, A. Alfi, and J. T. Machado, “Delay-dependent stability analysis of the quad vector field fractional order quaternion-valued memristive uncertain neutral type leaky integrator echo state neural networks,” Neural Network., vol. 117, pp. 307–327, 2019. https://doi.org/10.1016/j.neunet.2019.05.015.Search in Google Scholar PubMed

[45] W. Chartbupapan, O. Bagdasar, and K. Mukdasai, “A novel delay-dependent asymptotic stability conditions for differential and Riemann–Liouville fractional differential neutral systems with constant delays and nonlinear perturbation,” Mathematics, vol. 8, no. 1, p. 82, 2020. https://doi.org/10.3390/math8010082.Search in Google Scholar

[46] M. Iqbal, M. Rehan, K.-S. Hong, A. Khaliq, and S. ur Rehman, “Sector-condition-based results for adaptive control and synchronization of chaotic systems under input saturation,” Chaos, Solit. Fractals, vol. 77, pp. 158–169, 2015. https://doi.org/10.1016/j.chaos.2015.05.021.Search in Google Scholar

[47] H. Li, C. Li, D. Ouyang, and S. K. Nguang, “Impulsive stabilization of nonlinear time-delay system with input saturation via delay-dependent polytopic approach,” IEEE Trans. Systems, Man Cybernetics: Syst., pp. 1–12, 2020. https://doi.org/10.1109/tsmc.2019.2963398.Search in Google Scholar

[48] X. Yang, B. Zhou, F. Mazenc, and J. Lam, “Global stabilization of discrete-time linear systems subject to input saturation and time delay,” IEEE Trans. Automatic Control, vol. 66, no. 3, pp. 1345–1352, 2020.10.1109/TAC.2020.2989791Search in Google Scholar

[49] E. S. A. Shahri, A. Alfi, and J. T. Machado, “Stabilization of fractional-order systems subject to saturation element using fractional dynamic output feedback sliding mode control,” J. Comput. Nonlinear Dynam., vol. 12, no. 3, p. 031014, 2017. https://doi.org/10.1115/1.4035196.Search in Google Scholar

[50] E. S. A. Shahri, A. Alfi, and J. T. Machado, “Robust stability and stabilization of uncertain fractional order systems subject to input saturation,” J. Vib. Contr., vol. 24, no. 16, pp. 3676–3683, 2018. https://doi.org/10.1177/1077546317708927.Search in Google Scholar

[51] E. S. A. Shahri, A. Alfi, and J. T. Machado, “An extension of estimation of domain of attraction for fractional order linear system subject to saturation control,” Appl. Math. Lett., vol. 47, pp. 26–34, 2015. https://doi.org/10.1016/j.aml.2015.02.020.Search in Google Scholar

[52] E. S. A. Shahri, A. Alfi, and J. T. Machado, “Lyapunov method for the stability analysis of uncertain fractional-order systems under input saturation,” Appl. Math. Model., vol. 81, pp. 663–672, 2020. https://doi.org/10.1016/j.apm.2020.01.013.Search in Google Scholar

[53] E. S. A. Shahri, A. Alfi, and J. T. Machado, “Stability analysis of a class of nonlinear fractional-order systems under control input saturation,” Int. J. Robust Nonlinear Control, vol. 28, no. 7, pp. 2887–2905, 2018. https://doi.org/10.1002/rnc.4055.Search in Google Scholar

[54] S. Song, J. H. Park, B. Zhang, and X. Song, “Adaptive hybrid fuzzy output feedback control for fractional-order nonlinear systems with time-varying delays and input saturation,” Appl. Math. Comput., vol. 364, p. 124662, 2020. https://doi.org/10.1016/j.amc.2019.124662.Search in Google Scholar

[55] Z. Chen, J. Cheng, J. Tan, and Z. Cao, “Decentralized finite-time control for linear interconnected fractional-order systems with input saturation,” J. Franklin Inst., vol. 357, pp. 6137–6153, 2020. https://doi.org/10.1016/j.jfranklin.2020.04.018.Search in Google Scholar

[56] Y.-H. Lim, K.-K. Oh, and H.-S. Ahn, “Stability and stabilization of fractional-order linear systems subject to input saturation,” IEEE Trans. Automat. Contr., vol. 58, no. 4, pp. 1062–1067, 2012.10.1109/TAC.2012.2218064Search in Google Scholar

[57] D. Valério, J. J. Trujillo, M. Rivero, J. T. Machado, and D. Baleanu, “Fractional calculus: a survey of useful formulas,” Eur. Phys. J. Spec. Top., vol. 222, no. 8, pp. 1827–1846, 2013. https://doi.org/10.1140/epjst/e2013-01967-y.Search in Google Scholar

[58] E. S. A. Shahri and S. Balochian, “Analysis of fractional-order linear systems with saturation using Lyapunov second method and convex optimization,” Int. J. Autom. Comput., vol. 12, no. 4, pp. 440–447, 2015. https://doi.org/10.1007/s11633-014-0856-8.Search in Google Scholar

[59] I. R. Petersen, “A stabilization algorithm for a class of uncertain linear systems,” Syst. Contr. Lett., vol. 8, no. 4, pp. 351–357, 1987. https://doi.org/10.1016/0167-6911(87)90102-2.Search in Google Scholar

[60] K. Gu, J. Chen, and V. L. Kharitonov, Stability of Time-Delay Systems, Boston, Springer Science & Business Media, 2003.10.1007/978-1-4612-0039-0Search in Google Scholar

[61] S. Liu, W. Jiang, X. Li, and X.-F. Zhou, “Lyapunov stability analysis of fractional nonlinear systems,” Appl. Math. Lett., vol. 51, pp. 13–19, 2016. https://doi.org/10.1016/j.aml.2015.06.018.Search in Google Scholar

[62] F. Zhang, The Schur Complement and its Applications, vol. 4, United States of America, Springer Science & Business Media, 2006.Search in Google Scholar

[63] X. Liao, G. Chen, and E. N. Sanchez, “LMI-based approach for asymptotically stability analysis of delayed neural networks,” IEEE Trans. Circuits Syst. I, vol. 49, no. 7, pp. 1033–1039, 2002. https://doi.org/10.1109/tcsi.2002.800842.Search in Google Scholar

[64] A. Elahi and A. Alfi, “Finite-time H∞ stability analysis of uncertain network-based control systems under random packet dropout and varying network delay,” Nonlinear Dynam., vol. 91, pp. 713–731, 2017. https://doi.org/10.1007/s11071-017-3905-3.Search in Google Scholar

[65] K. Diethelm and N. J. Ford, “Analysis of fractional differential equations,” J. Math. Anal. Appl., vol. 265, no. 2, pp. 229–248, 2002. https://doi.org/10.1006/jmaa.2000.7194.Search in Google Scholar

[66] S. Bhalekar and V. Daftardar-Gejji, “A predictor-corrector scheme for solving nonlinear delay differential equations of fractional order,” J. Fractional Calculus Appl., vol. 1, no. 5, pp. 1–9, 2011.10.1155/2011/250763Search in Google Scholar