This paper focuses on the issue of stabilization of nonlinear fractional order time-delay systems in the presence of fault. A general class of nonlinear fractional order systems is considered in which fault causes variations in the system dynamic and actuators. Besides, time-varying delay is noticed in the system equations that is of high importance in control of real-life systems. In order to facilitate the problem of controller design for such systems, a precise method for modeling complex nonlinear systems, namely, Takagi–Sugeno fuzzy model, is adopted. Regarding a Caputo derivative–based Lyapunov–Krasovskii functional, new delay-dependent stabilization conditions are established in the form of linear matrix inequalities. Eventually, two examples including a truck–trailer and Lorenz system are simulated in order to evaluate the results of this research work.
AbbaspourAMokhtariSSargolzaeiA, et al. (2020) A survey on active fault-tolerant control systems. Electronics9(9): 1513.
2.
AbelNH (1823) Oplösning af et par opgaver ved hjelp af bestemte integraler. Magazin for naturvidenskaberne2: 55–68.
3.
Aguila-CamachoNDuarte-MermoudMAGallegosJA (2014) Lyapunov functions for fractional order systems. Communications in Nonlinear Science and Numerical Simulation19(9): 2951–2957.
4.
Naderi AkhormehAMoradiMaryamnegariHKhoshnoodAM, et al. (2021) Velocity estimation of flexible dynamics systems using virtual sensing. ISA transactions109: 242–258.
5.
ArfanMShahKUllahA, et al. (2021) On fractional order model of tumor dynamics with drug interventions under nonlocal fractional derivative. Results in Physics21: 103783.
6.
BushnaqSSaeedTTorresDF, et al. (2021) Control of covid-19 dynamics through a fractional-order model. Alexandria Engineering Journal60(4): 3587–3592.
7.
CaoYYFrankPM (2001) Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi–Sugeno fuzzy models. Fuzzy sets and systems124(2): 213–229.
8.
CaputoM (1967) Linear models of dissipation whose Q is almost frequency independent—II. Geophysical Journal International13(5): 529–539.
9.
ChenLHeYChaiY, et al. (2014) New results on stability and stabilization of a class of nonlinear fractional-order systems. Nonlinear Dynamics75(4): 633–641.
10.
ChenLWuRHeY, et al. (2015) Robust stability and stabilization of fractional-order linear systems with polytopic uncertainties. Applied mathematics and computation257: 274–284.
11.
ChenLWuRChengY, et al. (2020) Delay-dependent and order-dependent stability and stabilization of fractional-order linear systems with time-varying delay. IEEE Transactions on Circuits and Systems II: Express Briefs67(6): 1064–1068.
12.
ChenPWangBTianY, et al. (2022) Mittag–Leffler stability and finite-time control for a fractional-order hydraulic turbine governing system with mechanical time delay: an linear matrix inequalitie approach. Journal of Vibration and Control28(13–14): 1643–1654.
13.
ChengYHuTLiY, et al. (2021) Delay-dependent consensus criteria for fractional-order Takagi–Sugeno fuzzy multi-agent systems with time delay. Information Sciences560: 456–475.
14.
GuKChenJKharitonovVL (2003) Stability of Time-Delay Systems. Berlin, Germany: Springer Science & Business Media.
15.
HanHHanHGZhaoD, et al. (2022) Takagi-Sugeno fuzzy realization of stability performance-based fault-tolerant control for nonlinear systems. IEEE Transactions on Fuzzy Systems30: 4249–4261.
16.
IjazSIjazHHamayunMT, et al. (2022) Active and passive fault tolerant control allocation strategy for nonlinear systems. Journal of Vibration and Control: 107754632210977. Online ahead of print.
17.
LiouvilleJ (1832) Mémoire sur quelques questions de géométrie et de mécanique, et sur un nouveau genre de calcul pour résoudre ces questions. Journal de l’École Polytechnique, Paris13: 1–69.
18.
MahmoudabadiPTavakoli-KakhkiM (2021) Tracking control with disturbance rejection of nonlinear fractional order fuzzy systems: modified repetitive control approach. Chaos, Solitons & Fractals150: 111142. DOI: 10.1016/j.chaos.2021.111142.
19.
MahmoudabadiPTavakoli-KakhkiM (2022a) Fuzzy observer–based disturbance rejection control for nonlinear fractional-order systems with time-varying delay. Journal of Vibration and Control28(15–16): 2145–2154.
20.
MahmoudabadiPTavakoli-KakhkiM (2022b) Improved stability criteria for nonlinear fractional order fuzzy systems with time-varying delay. Soft Computing26: 4215–4226. DOI: 10.1007/s00500-022-06893-4.
21.
MahmoudabadiPTavakoli-KakhkiMAzarmiR (2022a) Delayed state-feedback fuzzy control for nonlinear fractional order systems: an LMI approach. In: 2022 23rd International Carpathian Control Conference (ICCC), Sinaia, Romania, May 29–Jun 01, 2022, pp. 37–42.
22.
MahmoudabadiPTavakoli-KakhkiMHosseinNiaSH (2022b) Fuzzy model-based disturbance rejection control for atomic force microscopy with input constraint. Journal of Vibration and Control29: 597–610. DOI: 10.1177/10775463211050157.
23.
Naderi AkhormehARoshanianJMoradiMaryamnegariH, et al. (2019) Online and stable parameter estimation based on normalized brain emotional learning model (nbelm). International Journal of Adaptive Control and Signal Processing33(7): 1047–1065.
24.
PanYWuYLamHK (2022) Security-based fuzzy control for nonlinear networked control systems with dos attacks via a resilient event-triggered scheme. IEEE Transactions on Fuzzy Systems30: 4359–4368.
25.
PengCFeiMR (2013) An improved result on the stability of uncertain T–S fuzzy systems with interval time-varying delay. Fuzzy Sets and Systems212: 97–109.
26.
PetersenIRHollotCV (1986) A Riccati equation approach to the stabilization of uncertain linear systems. Automatica22(4): 397–411.
27.
PhatVNiamsupPThuanMV (2020) A new design method for observer-based control of nonlinear fractional-order systems with time-variable delay. European Journal of Control56: 124–131.
28.
PodlubnyI (1998) Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications. Amsterdam, Netherlands: Elsevier.
29.
SakthivelRAhnCKJobyM (2019) Fault-tolerant resilient control for fuzzy fractional order systems. IEEE Transactions on Systems, Man, and Cybernetics: Systems49(9): 1797–1805.
30.
SongJHeX (2021) Model-based fault diagnosis of networked systems: a survey. Asian Journal of Control24: 526–536.
31.
SundarrajanSPalanisamiD (2021) Adaptive fault-tolerant control for fractional-order fuzzy financial time-delay system. Asian Journal of Control24: 3252–3261.
32.
SweethaSSakthivelRAlmakhlesDJ, et al. (2022) Non-fragile fault-tolerant control design for fractional-order nonlinear systems with distributed delays and fractional parametric uncertainties. IEEE Access10: 19997–20007.
33.
TakagiTSugenoM (1985) Fuzzy identification of systems and its applications to modeling and control. IEEE transactions on systems, man, and cybernetics15(1): 116–132.
34.
TrigeassouJCMaamriNSabatierJ, et al. (2011) A Lyapunov approach to the stability of fractional differential equations. Signal Processing91(3): 437–445.
35.
WangYGuLXuY, et al. (2016) Practical tracking control of robot manipulators with continuous fractional-order nonsingular terminal sliding mode. IEEE Transactions on Industrial Electronics63(10): 6194–6204.
36.
XuYGaoSLiW (2020) Exponential stability of fractional-order complex multi-links networks with aperiodically intermittent control. IEEE Transactions on Neural Networks and Learning Systems32(9): 4063–4074.
37.
XuYYuJLiW, et al. (2021) Global asymptotic stability of fractional-order competitive neural networks with multiple time-varying-delay links. Applied Mathematics and Computation389: 125498.
38.
XuYLinTLiuX, et al. (2022) Exponential bipartite synchronization of fractional-order multilayer signed networks via hybrid impulsive control. In: IEEE Transactions on Cybernetics. Piscataway, NJ: IEEE, pp. 1–13.
39.
YangWYuWZhengWX (2022) Fault-tolerant adaptive fuzzy tracking control for nonaffine fractional-order full-state-constrained miso systems with actuator failures. IEEE Transactions on Cybernetics52: 8439–8452.
40.
ZhangXHuangWWangQG (2021) Robust h∞ adaptive sliding mode fault tolerant control for ts fuzzy fractional order systems with mismatched disturbances. IEEE Transactions on Circuits and Systems I: Regular Papers68(3): 1297–1307.
41.
ZhengYNianYWangD (2010) Controlling fractional order chaotic systems based on Takagi–Sugeno fuzzy model and adaptive adjustment mechanism. Physics Letters A375(2): 125–129.
