Stability and global dissipativity for neutral-type fuzzy genetic regulatory networks with mixed delays. (English) Zbl 1476.93131
Summary: In this article, the stability and global dissipativity for neutral-type fuzzy genetic regulatory networks (FGRNs) with mixed time delays are investigated. By using Lyapunov functional method and linear matrix inequalities (LMIs) techniques, new sufficient conditions ensuring the stability and global dissipativity of the considered system are given. Moreover, the globally attractive set and positive invariant set are also presented here. The derived criteria are of the form of LMI and they can be checked by the numerically effect Matlab LMI toolbox. Lastly, two numerical examples with its simulations are proposed to illustrate the effectiveness of the obtained results. The derived results of this article are new and complement many earlier works and the ideas of this work can be applied to investigate other similar systems.
MSC:
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 93D20 | Asymptotic stability in control theory |
| 34D20 | Stability of solutions to ordinary differential equations |
| 34D23 | Global stability of solutions to ordinary differential equations |
| 93C42 | Fuzzy control/observation systems |
| 93A14 | Decentralized systems |
Keywords:
fuzzy genetic regulatory networks; asymptotic stability; global dissipativity; neutral-type; time delays; distributed delaysReferences:
| [1] | Ali, MS; Gunasekaran, N.; Ahn, CK; Shi, P., Sampled-data stabilization for fuzzy genetic regulatory networks with leakage delays, IEEE/ACM Trans Comput Biol Bioinform, 15, 1, 271-285 (2016) · doi:10.1109/TCBB.2016.2606477 |
| [2] | Aouiti, C.; Sakthivel, R.; Touati, F., Global dissipativity of high-order Hopfield bidirectional associative memory neural networks with mixed delays, Neural Comput Appl, 32, 14, 10183-10197 (2020) · doi:10.1007/s00521-019-04552-8 |
| [3] | Aouiti, C.; Sakthivel, R.; Touati, F., Global dissipativity of fuzzy cellular neural networks with inertial term and proportional delays, Int J Syst Sci, 51, 14, 1392-1405 (2020) · Zbl 1483.93518 · doi:10.1080/00207721.2020.1764128 |
| [4] | Aouiti, C.; Sakthivel, R.; Touati, F., Global dissipativity of fuzzy bidirectional associative memory neural networks with proportional delays, Iran J Fuzzy Syst, 18, 2, 65-80 (2021) · Zbl 1458.92005 |
| [5] | Aouiti C, Dridi F (2020) Delayed fuzzy genetic regulatory networks: novel results. Int J Biomath. doi:10.1142/S1793524521500285 · Zbl 1455.93165 |
| [6] | Cao, J.; Ren, F., Exponential stability of discrete-time genetic regulatory networks with delays, IEEE Trans Neural Netw, 19, 3, 520-523 (2008) · doi:10.1109/TNN.2007.911748 |
| [7] | Cao, Y.; Samidurai, R.; Sriraman, R., Stability and dissipativity analysis for neutral type stochastic Markovian jump static neural networks with time delays, J Artif Intell Soft Comput Res, 9, 2, 189-204 (2019) · doi:10.2478/jaiscr-2019-0003 |
| [8] | Ding, X.; Li, H.; Li, X.; Sun, W., Stability analysis of Boolean networks with stochastic function perturbations, IEEE Access, 7, 1323-1329 (2018) · doi:10.1109/ACCESS.2018.2885951 |
| [9] | Duan, L.; Di, F.; Wang, Z., Existence and global exponential stability of almost periodic solutions of genetic regulatory networks with time-varying delays, J Exp Theor Artif Intell, 32, 3, 453-463 (2020) · doi:10.1080/0952813X.2019.1652357 |
| [10] | He, W.; Cao, J., Robust stability of genetic regulatory networks with distributed delay, Cogn Neurodyn, 2, 4, 355-361 (2008) · doi:10.1007/s11571-008-9062-0 |
| [11] | Hu, J.; Liang, J.; Cao, J., Stabilization of genetic regulatory networks with mixed time-delays: an adaptive control approach, IMA J. Math. Control Inform., 32, 2, 343-358 (2015) · Zbl 1417.92045 · doi:10.1093/imamci/dnt048 |
| [12] | Li, P.; Lam, J., Disturbance analysis of nonlinear differential equation models of genetic SUM regulatory networks, IEEE/ACM Trans Comput Biol Bioinform, 8, 1, 253-259 (2010) |
| [13] | Ma, Y.; Zhang, Q.; Li, X., Dissipative control of markovian jumping genetic regulatory networks with time-varying delays and reaction-diffusion driven by fractional brownian motion, Differ Equ Dyn Syst, 28, 4, 841-864 (2020) · Zbl 1454.92015 · doi:10.1007/s12591-017-0349-7 |
| [14] | Manivannan, R.; Cao, Y., Design of generalized dissipativity state estimator for static neural networks including state time delays and leakage delays, J Franklin Inst, 355, 9, 3990-4014 (2018) · Zbl 1390.93607 · doi:10.1016/j.jfranklin.2018.01.051 |
| [15] | Plahte E, Gjuvsland AB, Omholt SW (2013) Propagation of genetic variation in gene regulatory networks. Phys D Nonlinear Phenom 256: 7-20. doi:10.1016/j.physd.2013.04.002 |
| [16] | Poblete, CM; Parra, FV; Gomez, JB; Saldias, MC; Garrido, SS; Vargas, HM, Fuzzy logic in genetic regulatory network models, Int J Comput Commun Control, 4, 4, 363-373 (2009) · doi:10.15837/ijccc.2009.4.2453 |
| [17] | Qiu, J.; Sun, K.; Yang, C.; Chen, X.; Chen, X.; Zhang, A., Finite-time stability of genetic regulatory networks with impulsive effects, Neurocomputing, 219, 9-14 (2017) · doi:10.1016/j.neucom.2016.09.017 |
| [18] | Rakkiyappan R, Balasubramaniam P, Balachandran K (2011) Delay-dependent global asymptotic stability criteria for genetic regulatory networks with time delays in the leakage term. Physica Scripta 84(5):055007 · Zbl 1262.34097 |
| [19] | Ram R, Chetty M, Dix TI (2006) Fuzzy model for gene regulatory network. In: 2006 IEEE International Conference on Evolutionary Computation (pp. 1450-1455). IEEE |
| [20] | Ratnavelu, K.; Kalpana, M.; Balasubramaniam, P., Stability analysis of fuzzy genetic regulatory networks with various time delays, Bull Malays Math Sci Soc, 41, 1, 491-505 (2018) · Zbl 1387.93131 · doi:10.1007/s40840-016-0427-y |
| [21] | Sakthivel, R.; Mathiyalagan, K.; Lakshmanan, S.; Park, JH, Robust state estimation for discrete-time genetic regulatory networks with randomly occurring uncertainties, Nonlinear Dyn, 74, 4, 1297-1315 (2013) · Zbl 1284.92076 · doi:10.1007/s11071-013-1041-2 |
| [22] | Sakthivel, R.; Joby, M.; Wang, C.; Kaviarasan, B., Finite-time fault-tolerant control of neutral systems against actuator saturation and nonlinear actuator faults, Appl Math Comput, 332, 425-436 (2018) · Zbl 1427.93213 |
| [23] | Selvi, S.; Sakthivel, R.; Mathiyalagan, K., Robust sampled-data control of uncertain switched neutral systems with probabilistic input delay, Complexity, 21, 5, 308-318 (2016) · doi:10.1002/cplx.21657 |
| [24] | Selvi, S.; Sakthivel, R.; Mathiyalagan, K., Delay-dependent robust reliable control for uncertain switched neutral systems, Complexity, 21, 5, 224-237 (2016) · doi:10.1002/cplx.21650 |
| [25] | Senthilraj, S.; Raja, R.; Zhu, Q.; Samidurai, R.; Zhou, H., Delay-dependent asymptotic stability criteria for genetic regulatory networks with impulsive perturbations, Neurocomputing, 214, 981-990 (2016) · doi:10.1016/j.neucom.2016.07.018 |
| [26] | Shen, H.; Huo, S.; Yan, H.; Park, JH; Sreeram, V., Distributed dissipative state estimation for Markov jump genetic regulatory networks subject to round-robin scheduling, IEEE Trans Neural Netw Learn Syst, 31, 3, 762-771 (2019) · doi:10.1109/TNNLS.2019.2909747 |
| [27] | Vasic, B.; Ravanmehr, V.; Krishnan, AR, An information theoretic approach to constructing robust Boolean gene regulatory networks, IEEE/ACM Trans Comput Biol Bioinform, 9, 1, 52-65 (2011) · doi:10.1109/TCBB.2011.61 |
| [28] | Wang, Z.; Liao, X.; Mao, J.; Liu, G., Robust stability of stochastic genetic regulatory networks with discrete and distributed delays, Soft Comput, 13, 12, 1199-1208 (2009) · Zbl 1176.92021 · doi:10.1007/s00500-009-0417-1 |
| [29] | Wang, H.; Qian, L.; Dougherty, E., Inference of gene regulatory networks using S-system: a unified approach, IET Syst Biol, 4, 2, 145-156 (2010) · doi:10.1049/iet-syb.2008.0175 |
| [30] | Wang, W.; Zhong, S.; Liu, F.; Cheng, J., Robust delay-probability-distribution-dependent stability of uncertain stochastic genetic regulatory networks with random discrete delays and distributed delays, Int J Robust Nonlinear Control, 24, 16, 2574-2596 (2014) · Zbl 1302.93233 · doi:10.1002/rnc.3011 |
| [31] | Wang, L.; Dong, Y.; Xie, D.; Cao, J., Global dissipativity for stochastic genetic regulatory networks with time-delays, IEEE Access, 8, 34880-34887 (2020) · doi:10.1109/ACCESS.2020.2974616 |
| [32] | Xu, C.; Aouiti, C.; Liu, Z., A further study on bifurcation for fractional order BAM neural networks with multiple delays, Neurocomputing, 417, 501-515 (2020) · doi:10.1016/j.neucom.2020.08.047 |
| [33] | Xu, C.; Liao, M.; Li, P.; Guo, Y.; Liu, Z., Bifurcation properties for fractional order delayed BAM neural networks, Cogn Comput, 13, 2, 322-356 (2021) · doi:10.1007/s12559-020-09782-w |
| [34] | Xu, C.; Liao, M.; Li, P.; Liu, Z.; Yuan, S., New results on pseudo almost periodic solutions of quaternion-valued fuzzy cellular neural networks with delays, Fuzzy Sets Syst, 411, 25-47 (2021) · Zbl 1467.34081 · doi:10.1016/j.fss.2020.03.016 |
| [35] | Xue, Y.; Zhang, L.; Zhang, X., Reachable set estimation for genetic regulatory networks with time-varying delays and bounded disturbances, Neurocomputing, 403, 203-210 (2020) · doi:10.1016/j.neucom.2020.03.113 |
| [36] | Yu, T.; Liu, J.; Zeng, Q.; Wu, L., Dissipativity-based filtering for switched genetic regulatory networks with stochastic disturbances and time-varying delays, IEEE/ACM Trans Comput Biol Bioinform, 18, 3, 1082-1092 (2021) · doi:10.1109/TCBB.2019.2936351 |
| [37] | Zhang, W.; Fang, JA; Tang, Y., New robust stability analysis for genetic regulatory networks with random discrete delays and distributed delays, Neurocomputing, 74, 14-15, 2344-2360 (2011) · doi:10.1016/j.neucom.2011.03.011 |
| [38] | Zhang, X.; Wu, L.; Cui, S., An improved integral inequality to stability analysis of genetic regulatory networks with interval time-varying delays, IEEE/ACM Trans Comput Biol Bioinform, 12, 2, 398-409 (2014) · doi:10.1109/TCBB.2014.2351815 |
| [39] | Zhang, X.; Wu, L.; Zou, J., Globally asymptotic stability analysis for genetic regulatory networks with mixed delays: an M-matrix-based approach, IEEE/ACM Trans Comput Biol Bioinform, 13, 1, 135-147 (2015) · doi:10.1109/TCBB.2015.2424432 |
| [40] | Zhang, L.; Zhang, X.; Xue, Y.; Zhang, X., New method to global exponential stability analysis for switched genetic regulatory networks with mixed delays, IEEE Trans NanoBiosci, 19, 2, 308-314 (2020) · doi:10.1109/TNB.2020.2971548 |
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