This paper studies the leader-following event-triggered consensus of multi-agent systems with nonlinear dynamics and semi-Markov jump. The information on transition rates is incompletely known. First, by applying weighted orthogonal polynomials, two new integral inequalities are established, which include some existing ones. Second, an event-triggered scheme is presented to save the precious communication resources. After constructing an augmented Lyapunov–Krasovskii functional, a few sufficient conditions are derived to achieve the leader-following event-triggered consensus by utilizing the presented inequalities to manipulate the derivative of the functional. Finally, numerical simulation shows the effectiveness of the proposed method.
ChenYShiY (2020) Distributed consensus of linear multiagent systems: Laplacian spectra-based method. IEEE Transactions on Systems, Man, and Cybernetics: System50(2): 700–706.
2.
CongMMuX (2019) H∞ consensus of linear multi-agent systems with semi-Markov switching network topologies and measurement noises. IEEE Access7: 156089–156096.
3.
DaiJGuoG (2018) Event-triggered leader-following consensus for multi-agent systems with semi-Markov switching topologies. Information Sciences459: 290–301.
4.
DingLGuoG (2015) Sampled-data leader-following consensus for nonlinear multi-agent systems with Markovian switching topologies and communication delay. Journal of the Franklin Institute352(1): 369–383.
5.
DingLZhengW (2017) Network-based practical consensus of heterogeneous nonlinear multiagent systems. IEEE Transactions on Cybernetics47(8): 1841–1851.
6.
GeXHanQLWangZ (2019) A threshold-parameter-dependent approach to designing distributed event-triggered H∞ consensus filters over sensor networks. IEEE Transactions on Cybernetics49(4): 1148–1159.
7.
GodsilCRoyleG (2001) Algebraic Graph Theory. New York: Springer-Verlag.
8.
HeMMuJMuX (2020a) H∞ leader-following consensus of nonlinear multi-agent systems under semi-Markovian switching topologies with partially unknown transition rates. Information Sciences513: 168–179.
9.
HeWXuBHanQL, et al. (2020b) Adaptive consensus control of linear multiagent systems with dynamic event-triggered strategies. IEEE Transactions on Cybernetics50(7): 2996–3008.
10.
HuaCSunXYouX, et al. (2017) Finite-time consensus control for second-order multi-agent systems without velocity measurements. International Journal of Systems Science48(2): 337–346.
11.
HuangJShiY (2013) Stochastic stability and robust stabilization of semi-Markov jump linear systems. International Journal of Robust and Nonlinear Control23(18): 2028–2043.
12.
HuangWTianBLiuT, et al. (2022) Event-triggered leader-following consensus of multi-agent systems under semi-Markov switching topology with partially unknown rates. Journal of the Franklin Institute359(7): 3103–3125.
13.
KimSHParkPJeongC (2010) Robust H∞ stabilisation of networked control systems with packet analyser. IET Control Theory & Applications4(9): 1828–1837.
14.
LiFDZhuQXuHT, et al. (2017) Stability analysis of delayed genetic regulatory networks via a relaxed double integral inequality. Mathematical Problems in Engineering2017: 1–16.
15.
LiuZZhangHZhangQ (2010) Novel stability analysis for recurrent neural networks with multiple delays via line integral-type L-K functional. IEEE Transactions on Neural Networks21(11): 1710–1718.
16.
MaGLiuXQinL, et al. (2016) Finite-time event-triggered H∞ control for switched systems with time-varying delay. Neurocomputing207: 828–842.
17.
ParkMJKwonOMParkJH, et al. (2015a) Stability of time-delay systems via Wirtinger-based double integral inequality. Automatica55: 204–208.
18.
ParkPGLeeWLeeSY (2015b) Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems. Journal of the Franklin Institute352(4): 1378–1396.
19.
SakthivelRParivallalATuanNH, et al. (2021) Nonfragile control design for consensus of semi-Markov jumping multiagent systems with disturbances. International Journal of Adaptive Control and Signal Processing35(6): 1039–1061.
20.
SeuretAGouaisbautF (2015) Hierarchy of LMI conditions for the stability analysis of time-delay systems. System & Control Letters81: 1–7.
21.
StoneLD (1973) Necessary and sufficient conditions for optimal control of semi-Markov jump processes. SIAM Journal on Control11(2): 187–201.
22.
WeiYParkJHQiuJ, et al. (2017) Sliding mode control for semi-Markovian jump systems via output feedback. Automatica81: 133–141.
23.
WuTHuangXChenX, et al. (2020) Sampled-data H∞ exponential synchronization for delayed semi-Markov jump CDNs: A looped-functional approach. Applied Mathematics and Computation377: 125156.
24.
XinBZhaoD (2021) GeneralizedH2 control of the linear system with semi-Markov jumps. International Journal of Robust and Nonlinear Control31(3): 1005–1020.
25.
ZhangCKHeYJiangL, et al. (2016) Stability analysis of systems with time-varying delay via relaxed integral inequalities. Systems & Control Letters92: 52–61.
26.
ZhangCKHeYJiangL, et al. (2017a) Delay-dependent stability analysis of neural networks with time-varying delay: A generalized free-weighting-matrix approach. Applied Mathematics and Computation294: 102–120.
27.
ZhangHLiuZHuangGB, et al. (2010) Novel weighting-delay-based stability criteria for recurrent neural networks with time-varying delay. IEEE Transactions on Neural Networks21(1): 91–106.
28.
ZhangHWangJWangZ, et al. (2017b) Sampled-data synchronization analysis of Markovian neural networks with generally incomplete transition rates. IEEE Transactions on Neural Networks and Learning Systems28(3): 740–752.
29.
ZhouJDongHFengJ (2017) Event-triggered communication for synchronization of Markovian jump delayed complex networks with partially unknown transition rates. Applied Mathematics and Computation293: 617–629.
