In this present paper, the event-triggered sliding mode control (SMC) issue for a type of singular networked Markov jump systems with partly unknown transition probabilities (TPs) is mainly investigated, and it is modeled by discrete-time Takagi–Sugeno fuzzy systems. To save network resources, a mode-dependent event-triggered scheme (ETS) is applied to improve transmission efficiency. Subsequently, a common sliding surface is designed, which can effectively reduce the impact of the jumping process. Therein, the stochastic admissibility criterion for the system with performance is derived in the sense of partly unknown TPs. Moreover, a novel SMC law that guarantees the reachability of the quasi-sliding mode is given in view of the reaching condition. Finally, the validity of the presented theorems is demonstrated by a numerical example.
Ben YazidYMehdiDNouriAS (2018) Discrete T-S fuzzy systems with time-varying delays: A new discrete sliding mode control approach. Transactions of the Institute of Measurement and Control40(7): 2332–2339.
2.
BoukasEKLiuZ (2001) Robust H∞ control of discrete-time Markovian jump linear systems with mode-dependent time-delays. IEEE Transactions on Automatic Control46(12): 1918–1924.
3.
ChanC (1999) Discrete adaptive quasi-sliding mode control. International Journal of Control72(4): 365–373.
4.
GhorbaniSSafaviAANaghaviSV (2021) Event-triggered robust model predictive control for lipschitz nonlinear networked control systems subject to communication delays. Transactions of the Institute of Measurement and Control43(5): 1126–1142.
5.
GhorbelCBenhadj BraiekN (2022) Nonfragile H∞ tracking control strategies for classes of linear and bilinear uncertain Takagi-sugeno fuzzy systems. Transactions of the Institute of Measurement and Control44(11): 2166–2176.
6.
HanYKaoYGaoC (2017) Robust sliding mode control for uncertain discrete singular systems with time-varying delays and external disturbances. Automatica75: 210–216.
7.
HanYKaoYParkJH (2019) Robust nonfragile observer-based control of switched discrete singular systems with time-varying delays: A sliding mode control design. International Journal of Robust and Nonlinear Control29(5): 1462–1483.
8.
JiangBKarimiHRKaoY, et al. (2019a) Takagi-Sugeno model based event-triggered fuzzy sliding-mode control of networked control systems with semi-Markovian switchings. IEEE Transactions on Fuzzy Systems28(4): 673–683.
9.
JiangBKarimiHRYangS, et al. (2019b) Takagi-sugeno model-based reliable sliding mode control of descriptor systems with semi-Markov parameters: Average dwell time approach. IEEE Transactions on Systems, Man, and Cybernetics: Systems51: 1549–1558.
10.
KaoYHanYZhuY, et al. (2023) Stability analysis of delayed discrete singular piecewise homogeneous Markovian jump systems with unknown transition probabilities via sliding mode approach. IEEE Transactions on Automatic Control69: 315–322.
11.
LamHKLeungFH (2005) Stability analysis of fuzzy control systems subject to uncertain grades of membership. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics)35(6): 1322–1325.
12.
LeeWIParkBYKimSH (2022) Relaxed observer-based stabilization and dissipativity conditions of ts fuzzy systems with nonhomogeneous Markov jumps via non-PDC scheme. Applied Mathematics and Computation434: 127455.
13.
LiuGParkJHXuS, et al. (2019) Robust non-fragile. H∞ Fault Detection Filter Design for Delayed Singular Markovian Jump Systems with Linear Fractional Parametric Uncertainties. Nonlinear Analysis: Hybrid Systems32: 65–78.
14.
LiuZChenXYuJ (2023) Adaptive sliding mode security control for stochastic Markov jump cyber-physical nonlinear systems subject to actuator failures and randomly occurring injection attacks. IEEE Transactions on Industrial Informatics19(3): 3155–3165.
15.
LiuZKarimiHRYuJ (2020) Passivity-based robust sliding mode synthesis for uncertain delayed stochastic systems via state observer. Automatica111: 108596.
16.
LuWHuangYHuM (2023) Markovian-jump reinforcement learning for autonomous underwater vehicles under disturbances with abrupt changes. Journal of Marine Science and Engineering11(2): 285.
17.
MaSBoukasEK (2009) Stability and robust stabilisation for uncertain discrete stochastic hybrid singular systems with time delay. IET Control Theory & Applications3(9): 1217–1225.
18.
MaYJiaXLiuD (2018) Finite-time dissipative control for singular discrete-time Markovian jump systems with actuator saturation and partly unknown transition rates. Applied Mathematical Modelling53: 49–70.
19.
MengXJiangBKarimiHR, et al. (2023) An event-triggered mechanism to observer-based sliding mode control of fractional-order uncertain switched systems. ISA Transactions135: 115–129.
20.
PalmRDriankovD (1998) Fuzzy switched hybrid systems-modeling and identification. In: Intelligent Control (ISIC), 1998. Held Jointly with IEEE International Symposium on Computational Intelligence in Robotics and Automation (CIRA), Intelligent Systems and Semiotics (ISAS), Proceedings, Gaithersburg, MD, 17 September, pp. 130–135. New York: IEEE.
21.
ShenMZhangGYuanY (2014) H∞ static output feedback controller design for continuous Markov jump systems with incomplete transition probabilities. Transactions of the Institute of Measurement and Control36(6): 743–753.
22.
ShenYWuZGShiP, et al. (2019) H∞ control of Markov jump time-delay systems under asynchronous controller and quantizer. Automatica99: 352–360.
23.
TakagiTSugenoM (1985) Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on Systems, Man, and Cybernetics15: 116–132.
24.
TanYLiuJXieX, et al. (2023) Event-triggered sliding-mode control for fuzzy semi-Markovian jump systems with dead zone input and application to circuit systems. IEEE Transactions on Circuits and Systems II: Express Briefs70: 3418–3423.
25.
UtkinVI (1993) Sliding mode control design principles and applications to electric drives. IEEE Transactions on Industrial Electronics40(1): 23–36.
26.
WangYLLimCCShiP (2016) Adaptively adjusted event-triggering mechanism on fault detection for networked control systems. IEEE Transactions on Cybernetics47(8): 2299–2311.
27.
XiaWXuSLuJ, et al. (2021) Event-triggered filtering for discrete-time Markovian jump systems with additive time-varying delays. Applied Mathematics and Computation391: 125630.
28.
XieWNguangSKZhuH, et al. (2022) A novel event-triggered asynchronous H∞ control for T-S fuzzy Markov jump systems under hidden Markov switching topologies. Fuzzy Sets and Systems443: 258–282.
29.
XueMYanHZhangH, et al. (2020) Event-triggered guaranteed cost controller design for T-S fuzzy Markovian jump systems with partly unknown transition probabilities. IEEE Transactions on Fuzzy Systems29(5): 1052–1064.
30.
YeZPanSZhouJ (2019) H∞ feedback controls based on discrete-time state observations for singular hybrid systems with nonhomogeneous Markovian jump. Journal of Applied Analysis & Computation9(5): 1750–1768.
31.
ZhangDJingYZhangQ, et al. (2020) Stabilization of singular T-S fuzzy Markovian jump system with mode-dependent derivative-term coefficient via sliding mode control. Applied Mathematics and Computation364: 124643.
32.
ZhangDNguangSKSrinivasanD, et al. (2017) Distributed filtering for discrete-time T-S fuzzy systems with incomplete measurements. IEEE Transactions on Fuzzy Systems26(3): 1459–1471.
33.
ZhangLZongGZhaoX, et al. (2023a) Reachable set control for discrete-time Takagi-Sugeno fuzzy singular Markov jump system. IEEE Transactions on Fuzzy Systems31: 3173–3184.
34.
ZhangMShiPMaL, et al. (2019) Network-based fuzzy control for nonlinear Markov jump systems subject to quantization and dropout compensation. Fuzzy Sets and Systems371: 96–109.
35.
ZhangPKaoYHuJ, et al. (2021) Robust observer-based sliding mode H∞ control for stochastic Markovian jump systems subject to packet losses. Automatica130: 109665.
36.
ZhangXLiuXSuH (2023b) Continuous sliding mode control for uncertain linear time-invariant systems with matched and unmatched uncertainties using the Lyapunov-function integral sliding mode. Transactions of the Institute of Measurement and Control45: 2501–2514.
37.
ZhangYXuSZouY, et al. (2011) Delay-dependent robust stabilization for uncertain discrete-time fuzzy Markovian jump systems with mode-dependent time delays. Fuzzy Sets and Systems164(1): 66–81.
