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Event-triggered guaranteed cost control for uncertain polytopic fractional-order systems subject to unknown time-varying delays. (English) Zbl 1536.34074

Summary: The problem of designing an event-triggered guaranteed cost controller for uncertain polytopic fractional-order systems subject to unknown time-varying delays is investigated in this paper. An event-triggered guaranteed cost controller is designed, and sufficient conditions for the existence of an event-triggered guaranteed cost state-feedback control for the considered systems are established. We provide a numerical example to demonstrate the effectiveness of the proposed method.

MSC:

34K35 Control problems for functional-differential equations
34K37 Functional-differential equations with fractional derivatives
34K36 Fuzzy functional-differential equations
37C60 Nonautonomous smooth dynamical systems
Full Text: DOI

References:

[1] Aghayan, ZS; Alfi, A.; Machado, JA, LMI-based stability analysis of fractional order systems of neutral type with time varying delays under actuator saturation, Comput. Appl. Math., 40, 1-24, 2021 · Zbl 1476.34110 · doi:10.1007/s40314-021-01522-6
[2] Aghayan, ZS; Alfi, A.; Machado, JT, Guaranteed cost-based feedback control design for fractional-order neutral systems with input-delayed and nonlinear perturbations, Comput. Appl. Math., 131, 95-107, 2022
[3] Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear Matrix Inequalities in Systems and Control Theory, 1994, Philadelphia: SIAM, Philadelphia · Zbl 0816.93004 · doi:10.1137/1.9781611970777
[4] Chen, L.; Li, T.; Wu, R.; Lopes, AM; Machado, JA; Wu, K., Output-feedback-guaranteed cost control of fractional-order uncertain linear delayed systems, Comput. Appl. Math., 39, 1-18, 2020 · Zbl 1463.93078 · doi:10.1007/s40314-020-01247-y
[5] Coronel-Escamilla, A.; Gomez-Aguilar, JF; Escobar-Jimenez, RF; GuerreroRamirez, GV, On the trajectory tracking control for an SCARA robot manipulator in a fractional model driven by induction motors with PSO tuning, Multibody Syst. Dyn., 43, 257-277, 2018 · Zbl 1407.70014 · doi:10.1007/s11044-017-9586-3
[6] Dong, T.; Wang, A., Event-triggered consensus of nonlinear multi-agent systems with unknown external disturbance, Asian J. Control, 20, 1928-1937, 2019 · Zbl 1407.93018 · doi:10.1002/asjc.1682
[7] Ding, Z.; Zeng, Z.; Zhang, H.; Wang, L., New results on passivity of fractional-order uncertain neural networks, Neurocomputing, 351, 51-59, 2019 · doi:10.1016/j.neucom.2019.03.042
[8] Du, F.; Lu, JG, New criteria on finite-time stability of fractional-order hopfield neural networks with time delays, IEEE Trans. Neural Netw. Learn. Syst., 9, 3858-3866, 2020
[9] Du, F.; Lu, JG, New approach to finite-time stability for fractional-order BAM neural networks with discrete and distributed delays, Chaos Solitons Fractals, 151, 2021 · Zbl 1498.34211 · doi:10.1016/j.chaos.2021.111225
[10] Du, F.; Lu, JG, Finite-time stability of fractional-order fuzzy cellular neural networks with time delays, Fuzzy Sets Syst., 438, 107-120, 2022 · Zbl 1522.93156 · doi:10.1016/j.fss.2021.08.011
[11] Feng, T.; Wu, B.; Liu, L.; Wang, YE, Finite-time stability and stabilization of fractional-order switched singular continuous-time systems, Circuits Syst. Signal Process., 38, 5528-5548, 2019 · doi:10.1007/s00034-019-01159-1
[12] Huong, DC; Thuan, MV; Hong, DT, New results on stability and stabilization of delayed Caputo fractional-order systems with convex polytopic uncertainties, J. Syst. Sci. Complex, 33, 563-583, 2020 · Zbl 1447.93272 · doi:10.1007/s11424-020-8338-2
[13] Huong, DC; Huynh, VT; Trinh, H., On static and dynamic triggered mechanisms for event-triggered control of uncertain systems, Circuits Syst. Signal Process., 39, 5020-5038, 2020 · Zbl 1485.93347 · doi:10.1007/s00034-020-01399-6
[14] Huong, DC, Event-triggered guaranteed cost control for uncertain neural networks systems with time delays, Circuits Syst. Signal Process., 40, 4759-4778, 2021 · Zbl 1509.93043 · doi:10.1007/s00034-021-01701-0
[15] Kilbas, A.; Srivastava, H.; Trujillo, J., Theory and Application of Fractional Diffrential Equations, 2006, San Diego: Elsevier, San Diego · Zbl 1092.45003
[16] Liu, L.; Cao, X.; Fu, Z.; Song, S.; Xing, H., Guaranteed cost finite-time control of fractional-order nonlinear positive switched systems with D-perturbations via MDADT, J. Syst. Sci. Complex, 32, 857-874, 2019 · Zbl 1414.93147 · doi:10.1007/s11424-018-7347-x
[17] Liu, L.; Di, Y.; Shang, Y.; Fu, Z.; Fan, B., Guaranteed cost and finite-time non-fragile control of fractional-order positive switched systems with asynchronous switching and impulsive moments, Circuits Syst. Signal Process., 40, 3143-3160, 2021 · Zbl 1508.93163 · doi:10.1007/s00034-020-01618-0
[18] Liu, Z.; Lou, X.; Wu, W.; Zhao, J., Event-triggered dynamic output feedback control for genetic regulatory network systems, Circuits Syst. Signal Process., 41, 3172-3198, 2022 · Zbl 1509.93018 · doi:10.1007/s00034-021-01951-y
[19] Lou, Y.; Xiao, X.; Cao, J.; Li, A., Event-triggered guaranteed cost consensus for uncertain nonlinear multi-agent systems with time delay, Neurocomputing, 394, 13-26, 2020 · doi:10.1016/j.neucom.2020.02.003
[20] Luo, D.; Tian, M.; Zhu, Q., Some results on finite-time stability of stochastic fractional-order delay differential equations, Chaos Solitons Fractals, 158, 2022 · Zbl 1505.93225 · doi:10.1016/j.chaos.2022.111996
[21] Mathiyalagan, K.; Balachandran, K., Finite-time stability of fractional-order stochastic singular systems with time delay and white noise, Complexity, 21, 370-379, 2016 · doi:10.1002/cplx.21815
[22] Merzoug, I.; Guezane-Lakoud, A.; Khaldi, R., Existence of solutions for a nonlinear fractional \(p\)-Laplacian boundary value problem, Rend. Circolo Mat. Palermo Ser., 2, 69, 1099-1106, 2020 · Zbl 1465.34033 · doi:10.1007/s12215-019-00459-4
[23] Niamsup, P.; Ratchagit, K.; Phat, VN, Novel criteria for finite-time stabilization and guaranteed cost control of delayed neural networks, Neurocomputing, 160, 281-286, 2015 · doi:10.1016/j.neucom.2015.02.030
[24] Shafiya, M.; Nagamani, G., Extended dissipativity criterion for fractional-order neural networks with time-varying parameter and interval uncertainties, Comput. Appl. Math., 41, 1-24, 2022 · Zbl 1513.93039 · doi:10.1007/s40314-022-01799-1
[25] Shang, Y.; Liu, L.; Di, Y.; Fu, Z.; Fan, B., Guaranteed cost and finite-time event-triggered control of fractional-order switched systems, Trans. Inst. Meas. Control, 43, 2724-2733, 2021 · doi:10.1177/01423312211004802
[26] Shen, W.; Xuhui, B.; Jiaqi, L., Event-triggered robust guaranteed cost control for two-dimensional nonlinear discrete-time systems, J. Syst. Eng. Electron., 30, 1243-1251, 2019 · doi:10.21629/JSEE.2019.06.18
[27] Tao, B.; Xiao, M.; Sun, Q.; Cao, J., Hopf bifurcation analysis of a delayed fractional-order genetic regulatory network model, Neurocomputing, 275, 677-6864, 2018 · doi:10.1016/j.neucom.2017.09.018
[28] Thuan, MV; Huong, DC, Robust guaranteed cost control for time-delay fractional-order neural networks systems, Optim. Control Appl. Meth., 40, 613-625, 2019 · Zbl 1425.93085 · doi:10.1002/oca.2497
[29] Thuan, MV; Binh, TN; Huong, DC, Finite-time guaranteed cost control of Caputo fractional-order neural networks, Asian J. Control, 22, 696-705, 2020 · Zbl 07872617 · doi:10.1002/asjc.1927
[30] Thuan, MV; Niamsu, P.; Phat, VN, Finite-time control analysis of nonlinear fractional-order systems subject to disturbances, Bull. Malays. Math. Sci. Soc., 44, 1425-1441, 2021 · Zbl 1466.34011 · doi:10.1007/s40840-020-01020-8
[31] Wang, J.; Yang, C.; Xia, J.; Wu, ZG; Shen, H., Observer-based sliding mode control for networked fuzzy singularly perturbed systems under weighted try-once-discard protocol, IEEE Trans. Fuzzy Syst., 30, 1889-1899, 2022 · doi:10.1109/TFUZZ.2021.3070125
[32] Weiss, L.; Infante, EF, On the stability of systems defined over a finite time interval, Proc. Natl. Acad. Sci. U.S.A., 1, 44-48, 1965 · Zbl 0134.30702 · doi:10.1073/pnas.54.1.44
[33] Yan, Z.; Zhang, G.; Wang, J.; Zhang, W., State and output feedback finite-time guaranteed cost control of linear Itô stochastic systems, J. Syst. Sci. Complex, 28, 813-829, 2015 · Zbl 1320.93084 · doi:10.1007/s11424-014-2178-x
[34] Yang, Y.; Chen, G., Finite-time stability of fractional order impulsive switched systems, Complexity, 25, 2207-2222, 2015 · Zbl 1328.93196
[35] Zhang, J.; Zhao, XD; Chen, Y., Finite-time stability and stabilization of fractional-order positive switched systems, Circuits Syst. Signal Process., 35, 2450-2470, 2016 · Zbl 1346.93204 · doi:10.1007/s00034-015-0236-9
[36] Zitane, H.; Larhrissi, R.; Boutoulout, A., Fractional output stabilization for a class of bilinear distributed systems, Rend. Circolo Mat. Palermo Ser., 2, 69, 737-752, 2020 · Zbl 1459.93151 · doi:10.1007/s12215-019-00429-w
[37] Zivanovic, MD; Vukobratovic, MK, Multi-arm Cooperating Robots: Dynamics and Control, 2006, Berlin: Spring, Berlin · Zbl 1113.93009
[38] Zong, G.; Ren, H., Guaranteed cost finite-time control for semi-Markov jump systems with event-triggered scheme and quantization input, Int. J. Robust Nonlinear Control, 29, 5251-5273, 2019 · Zbl 1426.93316 · doi:10.1002/rnc.4672
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