Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31515
Feedback Stabilization Based on Observer and Guaranteed Cost Control for Lipschitz Nonlinear Systems

Authors: A. Thabet, G. B. H. Frej, M. Boutayeb


This paper presents a design of dynamic feedback control based on observer for a class of large scale Lipschitz nonlinear systems. The use of Differential Mean Value Theorem (DMVT) is to introduce a general condition on the nonlinear functions. To ensure asymptotic stability, sufficient conditions are expressed in terms of linear matrix inequalities (LMIs). High performances are shown through real time implementation with ARDUINO Duemilanove board to the one-link flexible joint robot.

Keywords: Feedback stabilization, DMVT, Lipschitz nonlinear systems, nonlinear observer, real time implementation.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 959


[1] P. Schmidt, J. Moreno, and A. Schaum, “Observer design for a class of complex networks with unknown topoloy,” in World Congress The International Federation of Automatic Control, August 24-29, Cape Town, South Africa, 2014, pp. 2812–2817.
[2] H. Gripa, A. Saberi, and T. Johansenb, “Observers for interconnected nonlinear and linear systems,” Autmatica, vol. 48, p. 13391346, 2012.
[3] C. Kravaris and C. Chung, “Nonlinear state feedback synthesis by global input/output linearization,” AIChE J., vol. 33 (4), pp. 592–603, 1987.
[4] A. Teel and L. Praly, “Tools for smiglobal stabilization by partial state and output feedback,” SIAM J. Control Optim., vol. 33 (5), pp. 1443–1488, 1995.
[5] U. Cem and P. Kachroo, “Sliding mode measurement feedback control for antilock braking systems,” IEEE Trans. on Control. Syst. Technology, vol. 7 (2), pp. 271–281, 1999.
[6] A. Rodriguez and H. Nijmeijer, “Mutual synchronization of robots via estimated state feedback: A cooperative approach,” IEEE Trans. on Control. Syst. Technology, vol. 12 (4), pp. 542–554, 2004.
[7] Y. Li, T. Zheng, and Y. Li, “Extended state observer based adaptive back-stepping sliding mode control of electronic throttle in transportation cyber-physical systems,” Mathematical Problems in Eng., vol. doi:10.1155/2015/301656, pp. 1–11, 2015.
[8] L. Ghaoui, F. Oustry, and M. AItRami, “A cone complementarity linearization algorithm for static output-feedback and related problems,” IEEE Trans. on Autom. Control, vol. 42 (8), pp. 1171–1176, 1997.
[9] D. Fernandes, A. Sorensen, K. Pettersen, and D. Donha, “Output feedback motion control system for observation class rovs based on a high-gain state observer: Theoretical and experimental results,” Control Eng. Practice, vol. 39, pp. 90–102, 2015.
[10] B. Yao and M. Tomizuka, “Adaptive robust control of mimo nonlinear systems in semi-strict feedback forms,” Autmatica, vol. 37 (9), pp. 1305–1321, 2001.
[11] H. Khalil, “High-gain observers in nonlinear feedback control,” in Int. Conf. Control, Automation and Syst., Oct. 14-17, COEX, Seoul, Korea, 2008, pp. –.
[12] H. Khalil and L. Praly, “High-gain observer in nonlinear feedback control,” Int. J. of Robust. Nonlinear Control, vol. doi:10.1002/rnc.3051, pp. –, 2013.
[13] J. Yao, Z. Jiao, and D. Ma, “Extended state observer based output feedback nonlinear robust control of hydraulic systems with backstepping,” IEEE Trans. on Industrial Electronics, vol. 61 (11), pp. 6285–6293, 2014.
[14] H. Liu, T. Zhang, and X. Tian, “Continuous output-fedback finite time control for a class of second-order nonlinear systems with disturbances,” Int. J. of Robust. Nonlinear Control, vol. doi:10.1002/mc.3305, p. , 2015.
[15] S. Ge, C. Hang, and T. Zhang, “Adaptive neural network control of nonlinear systems by state and output feedback,” IEEE Trans. on Syst. Man and Cybernetics, vol. 29 (6), pp. 818–828, 1999.
[16] S. He, “Non fragile passive controller design for nonlinear markovian jumping systems via obserber-based control,” Neurocomputing, vol. 147, pp. 350–357, 2015.
[17] A. Zemouch and M. Boutayeb, “A unified H∞ adaptive observer synthesis method for a class of systems with both lipschitz and monotone nonlinearities,” Syst. Control Letters, vol. 58, pp. 282–288, 2009.
[18] A. Zemouch, M. Boutayeb, and G. Bara, “Observers for a class of lipschitz systems with extension to H∞ performance analysis,” Syst. Control Letters, vol. 57, pp. 18–27, 2008.
[19] A. Zemouch and M. Boutayeb, “On lmi conditions to design observers for lipschitz nonlinear systems,” Autmatica, vol. 49, pp. 585–591, 2013.
[20] N. Gasmi, A. Thabet, M. Boutayeb, and M. Aoun, “Observer design for a class of nonlinear discrete time systems,” in IEEE Int. Conf. on Sciences and Techniques of Automatic Control and Computer Engineering, Dec. 21-23, Monastir, Tunisia, 2015, pp. 799–804.
[21] G. Yang, J. Wang, and Y. Soh, “Reliable guaranteed cost control for uncertain nonlinear systems,” IEEE Trans. on Autom. Control, vol. 45, pp. 2188–3192, 2000.
[22] S. Boyd, L. E. Ghaoui, E. Ferron, and V. Balakrishnan, Linear matrix inequalities in systems and control theory, 15th ed. Philadelphia: Studies in Applied Mathematics SIAM, 1994.
[23] M. Spong, “Modeling and control of elastic joint robots,” Trans. ASME, J. Dyn. Syst., Meas. Control, vol. 109, pp. 310–319, 1987.