This paper further investigates the problem of reachable set estimation (RSE) for a class of continuous-time singular systems with time-varying delay. First, we use the relaxed Lyapunov–Krasovskii functional to tackle the RSE problem. This functional does not need all the matrices concerned to be positive definite. In addition, a novel weighted integral inequality and time-delay partition approach are utilized to reduce conservatism in the results. Based on these methods, sufficient conditions in the form of linear matrix inequalities are established. Finally, the correctness and validity of these relaxed results are demonstrated by three simulation examples.
DaiL (1989) Singular Control Systems. Cham: Springer.
2.
DingLHeDMiX, et al. (2021) A new relaxed Lyapunov-Krasovskii functional for stability analysis of time-varying delay systems. IEEE Access9: 130562–130569.
3.
FengZLamJ (2015) On reachable set estimation of singular systems. Automatica52: 146–153.
4.
FengZLiRBWuL (2024) Adaptive decentralized control for constrained strong interconnected nonlinear systems and its application to inverted pendulum. IEEE Transactions on Neural Networks and Learning Systems35(7): 10110–10120.
5.
FengZLiRBZhangN, et al. (2023) Event-based asymptotic tracking control for constrained MIMO nonlinear systems via a single-parameter adaptation method. IEEE Transactions on Systems, Man, and Cybernetics: Systems53(12): 7758–7768.
6.
GuoGAnXSunJ, et al. (2023) Observer-based event-triggered sliding mode tracking control for uncertain robotic manipulator systems. Journal of the Brazilian Society of Mechanical Sciences and Engineering45(9): 453.
7.
GuoGTanHFengY, et al. (2024) Event-triggered fixed-time tracking control for uncertain networked autonomous surface vehicle with disturbances. Ocean Engineering312: 119100.
8.
KimYGuDWPostlethwaiteI (2008) Real-time path planning with limited information for autonomous unmanned air vehicles. Automatica44(3): 696–712.
9.
LiFZhangX (2012) A delay-dependent bounded real lemma for singular LPV systems with time-variant delay. International Journal of Robust and Nonlinear Control22(5): 559–574.
10.
LiLHuangM (2023) Event-triggered consensus control for singular multi-agent systems based on observers. Transactions of the Institute of Measurement and Control45(9): 1661–1672.
11.
LiLZhangQZhuB (2015) Fuzzy stochastic optimal guaranteed cost control of bio-economic singular Markovian jump systems. IEEE Transactions on Cybernetics45(11): 2512–2521.
12.
LiYHeY (2021) New insight into admissibility analysis for singular systems with time-varying delays. International Journal of Systems Science52(13): 2752–2762.
13.
LiYHeYLinWJ, et al. (2020) Reachable set estimation for singular systems via state decomposition method. Journal of the Franklin Institute357(11): 7327–7342.
14.
LinBRenJ (2023) Robust preview control of nonlinear uncertain discrete-time time-delayed singular systems via sliding mode approach. Transactions of the Institute of Measurement and Control45(3): 440–451.
15.
LiuYDuGQuanQ, et al. (2016) Reachability calculation for aircraft maneuver using Hamilton-Jacobi function. Acta Automatica Sinica42(3): 347–357.
16.
LiuYWeiYWangC, et al. (2024) Trajectory optimization for adaptive deformed wheels to overcome steps using an improved hybrid genetic algorithm and an adaptive particle swarm optimization. Mathematics12(13): 2077.
17.
MaYZhangZYangL, et al. (2022) A resilient optimized dynamic event-triggered mechanism on networked control system with switching behavior under mixed attacks. Applied Mathematics and Computation430: 127300.
18.
ParkPKoJWJeongC (2011) Reciprocally convex approach to stability of systems with time-varying delays. Automatica47(1): 235–238.
19.
ShenZZhangLNiuB, et al. (2023) Event-based reachable set synthesis for delayed nonlinear semi-Markov systems. Chaos, Solitons & Fractals177: 114284.
20.
SongXZhangQZhangY, et al. (2022) Fuzzy event-triggered control for PDE systems with pointwise measurements based on relaxed Lyapunov–Krasovskii functionals. IEEE Transactions on Fuzzy Systems30: 3074–3084.
21.
ThapliyalOHwangI (2023) Approximating reachable sets for neural network-based models in real time via optimal control. IEEE Transactions on Control Systems Technology31(4): 1901–1908.
22.
TrinhH, et al. (2016) Exponential stability of time-delay systems via new weighted integral inequalities. Applied Mathematics and Computation275: 335–344.
23.
TangL.ZhangL.XuN. (2024). Optimized backstepping based finite-time containment control for nonlinear multi-agent systems with prescribed performance. Optimal Control Applications and Methods, 45(5), 2364–2382.
24.
WangXCaoYNiuB, et al. (2023) A novel bipartite consensus tracking control for multiagent systems under sensor deception attacks. IEEE Transactions on Cybernetics53: 5984–5993.
25.
WangYKarimiHRShenH, et al. (2018) Notice of violation of IEEE publication principles: Fuzzy-model-based sliding mode control of nonlinear descriptor systems. IEEE Transactions on Cybernetics49(9): 3409–3419.
26.
WangYXiaYShenH, et al. (2017) SMC design for robust stabilization of nonlinear Markovian jump singular systems. IEEE Transactions on Automatic Control63(1): 219–224.
27.
XuQGeL (2023) Dynamic event-triggered filtering for discrete-time singular networked control system subject to cyberattacks. Transactions of the Institute of Measurement and Control45(2): 363–373.
28.
YuanJGuoKMengL, et al. (2023) A distributionally robust optimization model for batch nonlinear switched time-delay system considering uncertain output measurements. Nonlinear Analysis: Hybrid Systems48: 101330.
29.
ZhangHZhaoNWangS, et al. (2023a) Improved event-triggered dynamic output feedback control for networked T–S fuzzy systems with actuator failure and deception attacks. IEEE Transactions on Cybernetics53(12): 7989–7999.
30.
ZhangLFengZJiangZ, et al. (2020) Improved results on reachable set estimation of singular systems. Applied Mathematics and Computation385: 125419.
31.
ZhangLShenZNiuB, et al. (2024) Dynamic-event-based reachable set synthesis for nonlinear delayed hidden semi-Markov jump systems under multiple cyber-attacks, IEEE Transactions on Systems, Man, and Cybernetics: Systems, DOI:10.1109/TSMC.2024.3485651.
32.
ZhangLZhangXZhaoX, et al. (2024b) Membership-function-dependent reachable set synthesis of Takagi-Sugeno fuzzy singular multi-agent systems subject to deception attacks. IEEE Transactions on Automation Science and Engineering. Epub ahead of print 27September. DOI: 10.1109/TASE.2024.3464580.
33.
ZhangLZhaoZMaZ, et al. (2024c) Prescribed performance adaptive neural event-triggered control for switched nonlinear cyber-physical systems under deception attacks. Neural Networks179: 106586.
34.
ZhangLZongGZhaoX, et al. (2023b) Reachable set control for discrete-time Takagi–Sugeno fuzzy singular Markov jump system. IEEE Transactions on Fuzzy Systems31(9): 3173–3184.
35.
ZhangPCaoJWangG (2014) Mode-independent guaranteed cost control of singular Markovian delay jump systems with switching probability rate design. International Journal of Innovative Computing Information and Control10(4): 1291–1303.
36.
ZhaoJ (2019) Algebraic criteria for reachable set estimation of delayed memristive neural networks. IET Control Theory & Applications13(11): 1736–1743.
37.
ZhaoNZhangHShiP (2024) Observer-based sampled-data adaptive tracking control for heterogeneous nonlinear multi-agent systems under denial-of-service attacks. IEEE Transactions on Automation Science and Engineering. Epub ahead of print 13June. DOI: 10.1109/TASE.2024.3411074.
38.
ZhiYLHeSZhangZM (2022) Further improvement for admissibility analysis of singular time-delay systems. IEEE Transactions on Systems, Man, and Cybernetics: Systems52: 4807–4812.
39.
ZongGSunXYangD, et al. (2023) Finite-time control for switched fuzzy systems: A dynamic adaptive event-triggered control approach. Fuzzy Sets and Systems464: 108475.
40.
ZongGYangDLamJ, et al. (2021) Fault-tolerant control of switched LPV systems: A bumpless transfer approach. IEEE/ASME Transactions on Mechatronics27(3): 1436–1446.
41.
ZuoZHoDWWangY (2010) Reachable set bounding for delayed systems with polytopic uncertainties: The maximal Lyapunov–Krasovskii functional approach. Automatica46(5): 949–952.
