Delay-dependent Robust Control for Uncertain Linear Systems with Distributed and Multiple Delays

Document Type : Research Article

Authors

1 Fasa University

2 Department of Biochemistry, University of Toronto

Abstract

This paper considers robust control of uncertain linear neutral systems with multiple state and state derivative delays. With equivalent descriptor representation, the stabilization problem is extended to more general class of neutral-type uncertain linear systems with discrete and distributed delays. The parametric uncertainties are time varying and unknown but norm bounded. Two delay-dependent/independent approaches are proposed to design robust controllers for a class of uncertain linear neutral systems with parametric uncertainty, discrete and distributed multiple delays. Using a presented descriptor model and an appropriate Lyapunov functional, sufficient conditions for closed loop stability are given in terms of linear matrix inequalities (LMIs). Solving the LMI problems, a robust memoryless state feedback is designed for all admissible uncertainties. The results depend on the size and varying rate of the delays. Two examples are provided to show the effectiveness of the proposed strategy.

Keywords

Main Subjects


[1] Richard, Jean-Pierre. "Time-delay systems: an overview of some recent advances and open problems." automatica 39.10 (2003): 1667-1694.
[2] Onyeka, Adrian E., Yan Xing-Gang, Zehui Mao, Bin Jiang, and Qingling Zhang. "Robust decentralised load frequency control for interconnected time delay power systems using sliding mode techniques." IET Control Theory & Applications 14, no. 3 (2019): 470-480.
[3] Zhang, Zhao, Huaguang Zhang, and Zhiliang Wang. "Non‐fragile robust control for networked control systems with long time‐varying delay, randomly occurring nonlinearity, and randomly occurring controller gain fluctuation." International Journal of Robust and Nonlinear Control 26, no. 1 (2016): 125-142.
[4] Curtain, Ruth F., and Hans Zwart. An introduction to infinite-dimensional linear systems theory. Vol. 21. Springer Science & Business Media, 2012.
[5] Li, Zhao-Yan, James Lam, and Yong Wang. "Stability analysis of linear stochastic neutral-type time-delay systems with two delays." Automatica 91 (2018): 179-189.
[6] Chinnamuniyandi, Maharajan, Raja Ramachandran, Jinde Cao, Grienggrai Rajchakit, and Xiaodi Li. "A new global robust exponential stability criterion for H∞ control of uncertain stochastic neutral-type neural networks with both timevarying delays." International Journal of Control, Automation and Systems 16, no. 2 (2018): 726-738.
[7] Duan, Wenyong, Baozhu Du, Yan Li, Cuifeng Shen, Xuelai Zhu, Xiaofan Li, and Jian Chen. "Improved sufficient LMI conditions for the robust stability of time-delayed neutral-type Lur’e systems." International Journal of Control, Automation and Systems 16, no. 5 (2018): 2343-2353..
[8] López-Labra, Héctor-Aristeo, Omar-Jacobo Santos-Sánchez, Liliam Rodríguez-Guerrero, Jesús-Patricio Ordaz-Oliver, and Carlos Cuvas-Castillo. "Experimental Results of Optimal and Robust Control for Uncertain Linear Time-Delay Systems." Journal of Optimization Theory and Applications 181, no. 3 (2019): 1076-1089.
[9] Xu, Chuanchuan, Bin Zhou, and Guang-Ren Duan. "Delayed output feedback of discrete-time time-delay systems with applications to spacecraft rendezvous." IET Control Theory & Applications 12, no. 6 (2018): 828-836.
[10] Fridman, Emilia. "New Lyapunov–Krasovskii functionals for stability of linear retarded and neutral type systems." Systems & control letters 43.4 (2001): 309-319.
[11] Lam, James, et al. "On global asymptotic stability for a class of delayed neural networks." International Journal of Circuit Theory and Applications 40.11 (2012): 1165-1174.
[12] Chen, Yonggang, Shumin Fei, and Yongmin Li. "Robust stabilization for uncertain saturated time-delay systems: a distributed-delay-dependent polytopic approach." IEEE Transactions on automatic control 62.7 (2016): 3455-3460.
[13] Lu, Renquan, Haiyi Wu, and Jianjun Bai. "New delay-dependent robust stability criteria for uncertain neutral systems with mixed delays." Journal of the Franklin Institute 351, no. 3 (2014): 1386-1399.
[14] Kharitonov, V. L. "Lyapunov functionals and Lyapunov matrices for neutral type time delay systems: a single delay case." International Journal of Control 78.11 (2005): 783-800.
[15] Sheikhlar, A., M. Zarghami, A. Fakharian, and M. B. Menhaj. "Delay compensation on fuzzy trajectory tracking control of omni-directional mobile robots." AUT Journal of Electrical Engineering 45, no. 2 (2015): 57-64.
[16] Ma, Yuechao, Pingjing Yang, and Qingling Zhang. "Delay-dependent robust absolute stability of uncertain Lurie singular systems with neutral type and time-varying delays." International Journal of Machine Learning and Cybernetics 9.12 (2018): 2071-2080.
[17] Krstic, Miroslav. "Lyapunov stability of linear predictor feedback for time-varying input delay." IEEE Transactions on Automatic Control 55.2 (2010): 554-559.
[18] Bekiaris-Liberis, Nikolaos. "Simultaneous compensation of input and state delays for nonlinear systems." Systems & Control Letters 73 (2014): 96-102.
[19] Shariati, Ala, and Mahdi Tavakoli. "A descriptor approach to robust leader-following output consensus of uncertain multi-agent systems with delay." IEEE Transactions on Automatic Control 62, no. 10 (2016): 5310-5317.
[20] Li, Xiaodi, and Shiji Song. "Stabilization of delay systems: delay-dependent impulsive control." IEEE Transactions on Automatic Control 62.1 (2016): 406-411.
[21] Chen, Wu-Hua, Wei Xing Zheng, and Yanjun Shen. "Delay-Dependent Stochastic Stability and $ H_ {infty} $-Control of Uncertain Neutral Stochastic Systems With Time Delay." IEEE Transactions on Automatic Control 54.7 (2009): 1660-1667.
[22] Shi, Guiju, et al. "Robust H2 guaranteed cost control of uncertain non-linear neutral systems with mixed delays." 2010 International Conference on Computer Application and System Modeling (ICCASM 2010). Vol. 7. IEEE, 2010.
[23] Zou, Jiahua, Yu Xue, Yantao Wang, and Xian Zhang. "Delay-dependent H∞ guaranteed cost control for uncertain neutral stochastic systems with unbounded distributed delays." In Proceedings of the 33rd Chinese Control Conference, pp. 4288-4293. IEEE, 2014.
[24] Ghadiri, Hamid, Mohammad Reza Jahed-Motlagh, and Mojtaba Barkhordari Yazdi. "Robust output observer-based guaranteed cost control of a class of uncertain switched neutral systems with interval time-varying mixed delays." International Journal of Control, Automation and Systems 12.6 (2014): 1167-1179.
[25] Wang, Ting, Tao Li, Guobao Zhang, and Shumin Fei. "New Lyapunov–Krasovskii functional for mixed-delay-dependent stability of uncertain linear neutral systems." Circuits, Systems, and Signal Processing 37, no. 5 (2018): 1825-1845.
[26] Kwon, O. M., Ju H. Park, and S. M. Lee. "An improved delay-dependent criterion for asymptotic stability of uncertain dynamic systems with time-varying delays." Journal of Optimization Theory and Applications 145.2 (2010): 343-353.
[27] Yue, D., & Won, S. "An improvement on delay and its time-derivative dependent robust stability of time-delayed linear systems with uncertainty". IEEE Transactions on Automatic Control. (2002), 47(2), 407-408.
[28] Boyd, Stephen, Laurent El Ghaoui, Eric Feron, and Venkataramanan Balakrishnan. Linear matrix inequalities in system and control theory. Society for industrial and applied mathematics, 1994.
[29] De Souza, Carlos E., and Xi Li. "Delay-dependent robust H∞ control of uncertain linear state-delayed systems." Automatica 35, no. 7 (1999): 1313-1321.
[30] El Fezazi, Nabil, El Houssaine Tissir, Fatima El Haoussi, Teresa Alvarez, and Fernando Tadeo. "Control based on saturated time-delay systems theory of mach number in wind tunnels." Circuits, Systems, and Signal Processing 37, no. 4 (2018): 1505-1522.
[31]Safa, Alireza, Mahdi Baradarannia, Hamed Kharrati, and Sohrab Khanmohammadi. "Fault Tolerant Control for Attitude Regulation of a Spacecraft with Delayed Feedback." AUT Journal of Electrical Engineering (2018).