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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 68 | Issue 8 | Year 2022 | Article Id. IJMTT-V68I8P505 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I8P505

Finite-Time Control of Nonlinear Switched Time-Varying Delay System


Xin Qi, Wenqin Wang
Received Revised Accepted Published
29 Jun 2022 30 Jul 2022 09 Aug 2022 22 Aug 2022
Abstract

In this paper, the boundedness and control of nonlinear switched time-varying delay systems in finite time are studied. By constructing a new Lyapunov-Krasovskii functional (LKF) and based on a new switching rule, sufficient conditions for the boundedness of the system in finite time and the calculation method of the state feedback controller are obtained. Finally, a numerical example is given to prove the feasibility of the proposed method.

Keywords
Time-varying delay, Switching system, Lyapunov-Krasovskii function, Finite time boundedness, Control
References

[1] F. Zhu and P. J. Antsaklis, “Optimal Control of Hybrid Switched Systems: A Brief Survey,” Discrete Event Dynamic Systems, vol. 25, no. 3, pp. 345-364, 2015.
[2] F. Xiao and L. Wang, “State Consensus for Multi-Agent Systems with Switching Topologies and Time-Varying Delays,” International Journal of Control, vol. 79, no. 10, pp. 1277-1284, 2006.
[3] J. Yu and L. Wang, “Group Consensus in Multi-Agent Systems with Switching Topologies and Communication Delays,” Systems and Control Letters, vol. 59, no. 6, pp. 340-348, 2010.
[4] W. Ni and D. Cheng, “Leader-Following Consensus of Multi-Agent Systems Under Fixed and Switching Topologies,” Systems and Control Letters, vol. 59, no. 3-4, pp. 209-217, 2010.
[5] D. Zheng, H. Zhang, J. Andrew Zhang, et al, “Consensus of the Second-Order Multi-Agent Systems Under Asynchronous Switching with a Controller Fault,” International Journal of Control, Automation and Systems, vol. 17, no. 1, pp. 136-144, 2019.
[6] Zhendong Sun, “Stabilization and Optimization of Switched Linear Systems,” Automatica., vol. 42, no. 5, pp. 783-788, 2006.
[7] Gholami. Hadi andBinazadeh, Tahereh, “Sliding-Mode Observer Design and Finite-Time Control of One-Sided Lipschitz Nonlinear Systems with Time-Delay,” Soft Computing, vol. 23, no. 15, pp. 6429-6440, 2018.
[8] Zhao. JM, Zhang. LJ and Qi. X, “A Necessary and Sufficient Condition for Stabilization of Switched Descriptor Time-Delay Systems Under Arbitrary Switching,”Asian Journal of Control, vol. 18, no. 1, pp. 266-272, 2016.
[9] Xiangze. Lin, Haibo. Du andShihua. Li, “Finite-time Boundedness and L2-Gain Analysis for Switched Delay Systems with NormBounded Disturbance,” Applied Mathematics and Computation, vol. 217, no. 12, pp. 5982-5993, 2011.
[10] Zhang. Xu, Wang. Jianfeng, Wu. Meixi andXu. Zhe, “Robust Quasi-Time Dependent Control for Switched Time-Delay Systems with Performance Guarantee,” Optimal Control Applications and Methods, vol. 41, no. 6, pp. 1831-1843, 2020.
[11] H. Gholami and M. H. Shafiei, “Finite-Time Boundedness and Stabilization of Switched Nonlinear Systems using Auxiliary Matrices and Average Dwell Time Method,” Trans. Inst. Meas. Control, vol. 42, no. 7, pp. 1406-1416, 2019.
[12] X. Zhao, Y. Yin, B. Niu and X. Zheng, “Stabilization for a Class of Switched Nonlinear Systems With Novel Average Dwell Time Switching by T-S Fuzzy Modeling,” IEEE Transactions on Cybernetics, vol. 46, no. 8, pp. 1952-1957, 2015.
[13] Zheng. Qunxian and Zhang. Hongbin, “Robust Stabilization of Continuous-Time Nonlinear Switched Systems without Stable Subsystems via Maximum Average Dwell Time,” Circuits, Systems, and Signal Processing, vol. 36, no. 4, pp. 1654-1670, 2017.
[14] Liu. Xingwen, Zhong. Shouming, Zhao. Qianchuan, “Dynamics of Delayed Switched Nonlinear Systems with Applications to Cascade Systems,” Automatica, vol. 87, pp. 251-257, 2018.
[15] Xingwen. Liu, “Stability Analysis of a Class of Nonlinear Positive Switched Systems with Delays,” Nonlinear Analysis: Hybrid Systems, vol. 16, pp. 1-12, 2015.
[16] T. C. Lee and Z. P. Jiang, “Uniform Asymptotic Stability of Nonlinear Switched Systems with an Application to Mobile Robots,” IEEE Transactions on Automatic Control, vol. 53, no. 5, pp. 1235-1252, 2008.
[17] B. D. O. Anderson, T. Brinsmead, D. Liberzon, et al, “Multiple Model Adaptive Control with Safe Switching,” International Journal of Adaptive Control and Signal Processing, vol. 15, no. 5, pp. 445-470, 2001.
[18] W. Gao andJ. C. Hung, “Variable Structure Control of Nonlinear Systems: A New Approach,” IEEE Transactions on Industrial Electronics, vol. 40, no. 1, pp. 45-55, 1993.
[19] Lijun. Gao andYuqiang. Wu, “A Design Scheme of Variable Structure -Infinity Control for Uncertain Singular Markov Switched Systems Based on Linear Matrix Inequality Method,” Nonlinear Analysis-Hybrid Systems, vol. 1, no. 3, pp. 306-316, 2007.
[20] He. S and Liu. F, “Finite-Time Fuzzy Control of Nonlinear Jump Systems with Time Delays via Dynamic Observer-Based State Feedback,” IEEE Trans. Fuzzy Syst., vol. 20, no. 4, pp. 605-614, 2012.
[21] Daizhan. Cheng, Lei. Guo, Yuandan. Lin and Yuan. Wang, “Stabilization of Switched Linear Systems,” IEEE Transactions on Automatic Control, vol. 50, no. 5, pp. 661-666, 2005.
[22] Gholami. Hadi and Shafiei. Mohammad Hossein, “Finite-Time H-Infinity Static and Dynamic Output Feedback Control for a Class of Switched Nonlinear Time-Delay Systems,” Applied Mathematics and Computation, vol. 389, pp. 125557, 2021.
[23] Gholami. H and Binazadeh. T, “Design Finite-Time Output Feed Back Controller for Nonlinear Discrete-Time Systems with TimeDelay and Exogenous Disturbances,” Systems Science and Control Engineering, vol. 6, no. 1, pp. 20-27, 2018.
[24] J. Song, Y. Niu and Y. Zou, “Finite-Time Stabilization via Sliding Mode Control,” IEEE Trans. Autom. Control, vol. 62, no. 3, pp. 1478-1483, 2017.
[25] H. Gholami and M. H. Shafiei, “Finite-Time Boundedness and Stabilization of Switched Nonlinear Systems using Auxiliary Matrices and Average Dwell Time Method,” Trans. Inst. Meas. Control, vol. 42, no. 7, pp. 1406-1416, 2019.

Citation :

Xin Qi, Wenqin Wang, "Finite-Time Control of Nonlinear Switched Time-Varying Delay System," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 8, pp. 39-45, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I8P505

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