Abstract
This paper investigates the problem of finite-time extended dissipative analysis and control for a class of uncertain switched time delay systems, where the uncertainties satisfy the polytopic form. By using the average dwell-time and linear matrix inequality technique, some sufficient conditions are proposed to guarantee that the switched system is finite-time bounded and has finite-time extended dissipative performance, where the H∞, L2-L∞, Passivity and (Q, S, R)-dissipativity performance can be solved simultaneously in a unified framework based on the concept of extended dissipative. Furthermore, a state feedback controller is presented to guarantee that the closed-loop system is finite-time bounded and satisfies the extended dissipative performance. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.
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References
H. Lin and P. J. Antsaklis, “Stability and stabilizability of switched linear systems: a survey of recent results,” IEEE Trans. Autom. Control, vol. 54, no. 2, pp. 308–322, 2009. [click]
D. Liberzon and A. S. Morse, “Basic problems in stability and design of switched systems,” IEEE Control Systems Magazine, vol. 19, pp. 59–70, 1999. [click]
X. D. Zhao, L. X. Zhang, P. Shi, and M. Liu, “Stability of switched positive linear systems with average dwell time switching,” Automatica, vol. 48, pp. 1132–1137, 2012. [click]
L. Lu, Z. L. Lin, and H. J. Fang, “L 2 gain analysis for a class of switched systems,” Automatica, vol. 45, pp. 965–972, 2009. [click]
X. D. Zhao, P. Shi, and L. X. Zhang, “Asynchronously switched control of a class of slowly switched linear systems,” Systems Control Letters, vol. 61, pp. 1151–1156, 2012. [click]
M. J. Hu, Y. W Wang, and J. W. Xiao, “Positive observer design for linear impulsive positive systems with interval uncertainties and time delay,” International Journal of Control, Automation and Systems, vol. 15, no. 3, pp. 1032–1039, 2017. [click]
Y. Zhang, H. Zhu, X. Liu, and S. Zhong. “Reliable H∞ control for a class of switched neutral systems,” Complex Syst Appl: Model. Control Simulat, vol. 14, no. S2, pp. 4–9, 2007.
D. Liu, S. Zhong, X. Liu, and Y. Huang. “Stability analysis for uncertain switched neutral systems with discrete timevarying delay: a delay-dependent method,” Math Comput Simulat., vol. 80, no. 8, pp. 28–39, 2009.
L. Xiong, S. Zhong, M. Ye, and S. Wu. “New stability and stabilization for switched neutral control systems,” Chaos Solitons Fract, vol. 42. no. 3, pp. 1800–11, 2009.
R. Wang, P. Shi, Z. G. Wu, and Y. T. Sun, “Stabilization of switched delay systems with polytopic uncertainties under asynchronous switching,” Journal of the Franklin Institute, vol. 350, pp. 2028–2043, 2013.
X. Lin, H. Du, and S. Li. “Finite-time boundedness and L 2-gain analysis for switched delay systems with normbounded disturbance,” Appl Math Comput., vol. 217(12), no. 59, pp. 82–93, 2011.
Z. Xiang, Y. Sun, and M.S. Mahmoud, “Robust finite-time H∞ control for a class of uncertain switched neutral systems,” Commun. Nonlinear Sci. Numer. Simul., vol. 17, no. 4, pp. 1766–1778, 2012. [click]
S. Wang, T. G Shi, L. X. Zhang, A. Jasra, and M. Zeng, “Extended finite-time H∞ control for uncertain switched linear neutral systems with time-varying delays,” Neurocomputing, vol. 152, pp. 377–387, 2015. [click]
S. Wang, M. Basin, L. X. Zhang, M. Zeng, T. Hayat, and A. Alsaedi, “Reliable finite-time filtering for impulsive switched linear systems with sensor failures,” Signal Processing, vol. 125, pp. 134–144, 2016. [click]
B. Y. Zhang, W. X. Zheng, and S. Y. Xu, “Filtering of Markovian jump delay systems based on a new performance index,” IEEE Trans. Circuits Syst. I Reg. Pap., vol. 60, pp. 1250–1263, 2013.
H. Shen, Y. Z. Zhu, L. X. Zhang, and J. H. Park, “Extended dissipative state estimation for Markov jump neural networks with unreliable links,” IEEE Trans. Neural Netw. Learning Syst., vol. 28, pp. 346–358, 2017.
J. Y. Xiao, Y. T Li, S. M Zhong, F Xu, et al., “Extended dissipative state estimation for memristive neural networks with time-varying delay,” ISA Transactions, vol. 64, pp. 113–128, 2016.
J. W. Xia, G. L. Chen, and W. Sun, “Extended dissipative analysis of generalized Markovian switching neural networks with two delay components,” Neurocomputing, vol. 260, pp. 275–283, 2017.
H. L. Yang, L. Shu, S. M. Zhong, and X. Wang, “Extended dissipative exponential synchronization of complex dynamical systems with coupling delay and sampled-data control,” Journal of the Franklin Institute, vol. 353, pp. 1829–1847, 2016. [click]
H. B. Zeng, K. L Teo, and Y. He, “A new looped-functional for stability analysis of sampled-data systems,” Automatica, vol. 82, pp. 328–331, 2017. [click]
S. P. Xiao, X. Z. Liu, C. F. Zhang, and H. B. Zeng, “Further results on absolute stability of Lur’e systems with a time-varying delay,” Neurocomputing, vol. 207, pp. 823–827, 2016. [click]
H. B. Zeng, Y. He, P. Shi, M. Wu, and S. P. Xiao, “Dissipativity analysis of neural networks with time-varying delays,” Neurocomputing, vol. 168, pp. 741–746, 2015. [click]
S. P. Xiao, H. H. Lian, H. B. Zeng, G. Chen, and W. H. Zheng, “Analysis on robust passivity of uncertain neural networks with time-varying delays via free-matrix-based integral inequality,” International Journal of Control, Automation and Systems, vol. 15, pp. 1–10, 2017.
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Recommended by Associate Editor Young Ik Son under the direction of Editor Duk-Sun Shim. This work was supported by Natural Science Foundation of China (No. 61573177, 61603170 and 61773191); the Natural Science Foundation of Shandong Province for Outstanding Young Talents in Provincial Universities under Grant (ZR2016JL025).
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Gao, H., Xia, J. & Zhuang, G. Robust Finite-time Extended Dissipative Control for a Class of Uncertain Switched Delay Systems. Int. J. Control Autom. Syst. 16, 1459–1468 (2018). https://doi.org/10.1007/s12555-017-0393-7
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DOI: https://doi.org/10.1007/s12555-017-0393-7