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

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2022 by IJMTT Journal
Volume-68 Issue-8
Year of Publication : 2022
Authors : Xin Qi, Wenqin Wang
 10.14445/22315373/IJMTT-V68I8P505

How to Cite?

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

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.

Reference

[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.