This paper addresses the problem of model-based global stability analysis of discrete-time Takagi-Sugeno multiregional dynamic output controllers with static antiwindup filters. The presented analyses are reduced to the problem of a feasibility study of the Linear Matrix Inequalities (LMIs), derived based on Lyapunov stability theory. Two sets of LMIs are considered candidate derived from the classical common quadratic Lyapunov function, which may in some cases be too conservative, and a fuzzy Lyapunov function candidate, which has been proven to significantly reduce the conservatism level, although at the cost of increasing the number of LMIs. Two numerical examples illustrate the main result.
@article{bwmeta1.element.bwnjournal-article-amcv23z1p65bwm,
author = {Tomasz Zubowicz and Mietek A. Brdy\'s},
title = {Stability of softly switched multiregional dynamic output controllers with a static antiwindup filter: A discrete-time case},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {23},
year = {2013},
pages = {65-73},
zbl = {1293.93583},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv23z1p65bwm}
}
Tomasz Zubowicz; Mietek A. Brdyś. Stability of softly switched multiregional dynamic output controllers with a static antiwindup filter: A discrete-time case. International Journal of Applied Mathematics and Computer Science, Tome 23 (2013) pp. 65-73. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv23z1p65bwm/
[000] Castelan, E., Leite, V., Miranda, M. and Moraes, V. (2010). Synthesis of output feedback controllers for a class of nonlinear parameter-varying discrete-time systems subject to actuator limitations, Proceedings of the American Control Conference, ACC 2010, Baltimore, MD, USA, pp. 4235-4240.
[001] Castelan, E., Moreno, U. and de Pieri, E. (2006). Absolute stabilisation of discrete-time systems with sector bounded nonlinearity under control saturations, IEEE International Symposium on Circuits and Systems, ISCAS 2006, Island of Kos, Greece, pp. 3105-3108.
[002] Domański, P., Brdyś, M.A. and Tatjewski, P. (1999). Design and stability of fuzzy logic multi-regional output controllers, International Journal of Applied Mathematics and Computer Science 9(4): 883-897. | Zbl 0938.93562
[003] Feng, G. (2006). A survey on analysis and design of model-based fuzzy control systems, IEEE Transaction on Fuzzy Systems 14(5): 676-697, DOI: 10.1109/TFUZZ.2006.883415.
[004] Gomes da Silva, Jr., J.M., Corso, J. and Castelan, E. (2008). Output feedback stabilization for systems presenting sector-bounded nonlinearities and saturating inputs, Proceedings of the 17th IFAC World Congress, Seoul, Korea, pp. 14109-14114.
[005] Gomes da Silva, Jr., J.M. and Tarbouriech, S. (2006). Anti-windup design with guaranteed regions of stability for discrete-time linear systems, System Control Letters 55(3): 184-192, DOI: 10.1016/j.sysconle.2005.07.001. | Zbl 1129.93385
[006] Han, Y., Brdyś, M. and Piotrowski, R. (2008). Nonlinear PI control for dissolved oxygen tracking at wastewater treatment plant, Proceedings of the IFAC World Congress, IFAC WC 2008, Seoul, Korea, DOI: 10.3182/20080706-5-KR-1001.0477.
[007] Khalil, H. (1996). Nonlinear Systems, 2nd Edn., Prentice-Hall, Upper Saddle River, NJ.
[008] Klug, M., Castelan, E. and Leite, V. (2011). A dynamic compensator for parameter varying systems subject to actuator limitations applied to a T-S fuzzy system, Proceedings of the IFAC World Congress, IFAC WC 2011, Milan, Italy, pp. 14495-14500.
[009] Qi, R. and Brdyś, M. (2008). Stable indirect adaptive control based on discrete-time T-S fuzzy model, Fuzzy Sets and Systems 159(8): 900-925, DOI: 10.1016/j.fss.2007.08.009. | Zbl 1170.93347
[010] Qi, R. and Brdys, M.A. (2009). Indirect adaptive controller based on a self-structuring fuzzy system for nonlinear modeling and control, International Journal of Applied Mathematics and Computer Science 19(4): 619-630, DOI: 10.2478/v10006-009-0049-8. | Zbl 1300.93100
[011] Rhee, B.-J. and Won, S. (2006). A new fuzzy Lyapunov function approach for Takagi-Sugeno fuzzy control systems design, Fuzzy Sets and Systems 157(9): 1211-1228, DOI:10.1016/j.fss.2005.12.020. | Zbl 1090.93025
[012] Tanaka, K., Ikeda, T. and Wang, H. (1998). Fuzzy regulators and fuzzy observers: Relaxed stability conditions and LMI-based design, Fuzzy Sets and Systems 6(2): 250-265, DOI: 10.1109/91.669023.
[013] Tanaka, K. and Sugeno, M. (1992). Stability analysis and design of fuzzy control systems, Fuzzy Sets and Systems 45(2): 135-156, DOI: 10.1016/0165-0114(92)90113-I. | Zbl 0758.93042
[014] Tatjewski, P. (2007). Advanced Control of Industrial Processes: Structures and Algorithms, Springer, London. | Zbl 1134.93037
[015] Wang, Y., Sun, Z. and Sun, F. (2004). Stability analysis and control of discrete-time fuzzy systems: A fuzzy Lyapunov function approach, Proceedings of the 5th Asian Control Conference, Melbourne, Australia, pp. 1855-1860, DOI: 10.1109/ASCC.2004.184913.
[016] Xiu, Z. and Ren, G. (2005). Stability analysis and systematic design of Takagi-Sugeno fuzzy control systems, Fuzzy Sets and Systems 151(1): 119-138, DOI: 10.1016/j.fss.2004.04.008. | Zbl 1142.93373
[017] Yaochu, J. (2002). Advanced Fuzzy Systems Design and Applications, Physica-Verlag, Heidelberg/New York, NY. | Zbl 1055.68083
[018] Zubowicz, T., Brdyś, M. and Piotrowski, R. (2010). Intelligent PI controller and its application to dissolved oxygen tracking problem, Journal of Automation, Mobile Robotics & Intelligent Systems 4(3): 16-24.