Volume 11, Issue 3 (Journal of Control, V.11, N.3 Fall 2017)
JoC 2017, 11(3): 35-49 |
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Bashiri S, Mobayen S, Bayat F. Observer Designing for Discrete-Time Piecewise Linear Systems: Linear Matrix Inequalities Approach. JoC 2017; 11 (3) :35-49
URL: http://joc.kntu.ac.ir/article-1-390-en.html
URL: http://joc.kntu.ac.ir/article-1-390-en.html
1- University of Zanjan
Abstract: (25463 Views)
In this paper, the state feedback and design problem of state observer are presented to stabilize the discrete-time piecewise linear systems. In this article, we have two discrete-time systems that one of them is the disturbed system and the other is the system without disturbance. The linear matrix inequalities approach, piecewise quadratic Lyapunov functions and the Finsler’s lemma are used to design the state observer. In addition to the above mentioned methods, H∞ control approach used to design the state observer for the system with external disturbance. The H∞ control approach undermines the disturbance signal and provides an appropriate estimation of the system states. In this paper, by using the Finsler’s lemma, a set of slack variables are introduced to reduce the design conservatism. The Simulation results show the high performance of the proposed method for stabilize the closed-loop system and achieve to the acceptable estimation of state variables.
Keywords: State observer, Static output feedback, Discrete-time systems, Linear matrix inequalities, Finsler’s lemma.
Type of Article: Research paper |
Subject:
Special
Received: 2016/07/21 | Accepted: 2017/07/16 | Published: 2017/08/29
Received: 2016/07/21 | Accepted: 2017/07/16 | Published: 2017/08/29
References
1. J. Xu and L. Xie, 2005,'' Null controllability of discrete-time planar bimodal piecewise linear systems,'' International Journal of Control, Taylor & Francis, pp.1486-1496.
2. M. Bernardo, U. Montanaro, J. M. Olm and S. Santini, 2012,''Model reference adaptive control of discrete-time piecewise linear systems,'' International Journal of Robust and Nonlinear Control, Wiley, vol.23, no.7, pp.709-730. [DOI:10.1002/rnc.2786]
3. W. Assawinchaichote, S. K. Nguang, P. Shi and E. Boukas, 2008,'' H∞ fuzzy state-feedback control design for nonlinear systems with D-stability constraints: an LMI approach,'' Mathematics and Computers in Simulation, Elsevier, vol.78, no.4, pp.514-531. [DOI:10.1016/j.matcom.2007.07.002]
4. B. Xu, Y. Xu and L. He, 2011,'' LMI-based stability analysis of impulsive high-order Hopfield-type neural networks,'' Mathematics and Computers in Simulation- Elsevier, vol.86, pp. 67-77.
5. S. Mobayen, 2015,''Optimal LMI-based state feedback stabilizer for uncertain nonlinear systems with time-varying uncertainties and disturbances,'' Complexity, vol.21, no.6.
6. AT. Nguyen, M. Sugeno and V. Campos, 2016,'' LMI-based stability analysis for piecewise multi-affine systems,'' IEEE Transactions on Fuzzy Systems, no.99.
7. D. Simon, 2006, Optimal State Estimation, Kalman, H∞, and Nonlinear Approaches. John Wiley & Sons, INC.
8. C. H. Lien, K. W. Yu, Y. F. Lin, Y. J. Chung and L. Y. Chung, 2008, ''Robust reliable H∞ control for uncertain nonlinear systems via LMI approach,'' Applied Mathematics and Computation-Elsevier, vol.198, no.1, pp.453-462. [DOI:10.1016/j.amc.2007.08.085]
9. S. Xu and T. Chen, 2004,''Robust H∞ control for uncertain discrete-time systems with time-varying delays via exponential output feedback controllers,'' Systems & Control Letters-Elsevier, vol.51, no.4, pp.171-183. [DOI:10.1016/j.sysconle.2003.08.002]
10. LK. Wang, HG. Zhang and XD. Liu, 2016,'' H∞ Observer design for continuous-time Takagi-Sugeno fuzzy model with unknown premise variables via nonquadratic lyapunov function,'' IEEE Transactions on Cybernetics, vol.48, no.9, pp.1986-1996. [DOI:10.1109/TCYB.2015.2459016]
11. مولف: ک. اوگاتا، ''سيستم هاي کنترل ديجيتال''، مترجمين: پ. جبه دار مارالاني و ع، خاکي صديق، موسسه انتشارات دانشگاه تهران، 1391 ، جلد 2، چاپ 7.
12. J. Li, Y. Liu, 2007, ''Stabilization of a class of discrete-time switched systems via observer-based output feedback,'' Journal of Control Theory and Applications, Springer, vol.5, no.3, pp.307-311. [DOI:10.1007/s11768-006-6064-5]
13. Z. Lendek, P. Raica and J. Lauber, 2014,'' Observer design for switching nonlinear systems,'' Fuzzy Systems (FUZZ-IEEE), 2014 IEEE International Conference on.
14. G. He, Y. Liu, J. Zhang, W. Yu, 2016,'' Robust observer-based fault estimation and tolerant control scheme for class of discrete piecewise systems,'' Intelligent Control and Automation (WCICA), 2016 12th World Congress on.
15. X. Du and G.H. Yang, 2010, '' Improved LMI conditions for H∞ output feedback stabilization of linear discrete-time systems,'' International Journal of Control, Automation and Systems, Springer, vol.8, no.1, pp.163-168. [DOI:10.1007/s12555-010-0121-z]
16. D. Da-Wei, Y. Guang-Hong, 2009, '' Static output feedback control for discrete-time piecewise linear systems: an LMI approach,'' Acta Automatica Sinica, Elsevier, vol.35, no.4, pp.337-344. [DOI:10.1016/S1874-1029(08)60080-4]
17. S. Ibrir and S. Diopt, 2008, ''Novel LMI conditions for observer-based stabilization of lipschitzian nonlinear systems and uncertain linear systems in discrete-time'', Applied Mathematics and Computation, Elsevier, vol.206, no.2, pp.579-588. [DOI:10.1016/j.amc.2008.05.150]
18. X. Du and G.H. Yang, 2009,'' New characterizations of positive realness and static output feedback control of discrete-time systems,'' International Journal of Control, Taylor & Francis, vol.82, no.8, pp.1485-1495. [DOI:10.1080/00207170802549586]
19. G Feng, M Chen and TJ Zhang, 2005,'' Observer design of piecewise discrete time linear systems,'' Control and Automation, 2005. ICCA '05. International Conference on.
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