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Global sampled-data output feedback control for a class of feedforward nonlinear systems. (English) Zbl 1313.93133

Summary: This paper investigates the problem of global output feedback stabilization for a class of feedforward nonlinear systems via linear sampled-data control. To solve the problem, we first construct a linear sampled-data observer and a controller. Then, a scaling gain is introduced into the proposed observer and controller. Finally, we use the sampled-data output feedback domination approach to find the explicit formula for choosing the scaling gain and the sampling period which renders the closed-loop system globally asymptotically stable. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.

MSC:

93C57 Sampled-data control/observation systems
93B52 Feedback control
93C10 Nonlinear systems in control theory
93D20 Asymptotic stability in control theory
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References:

[1] A. Teel. Using saturation to stabilize a class of single-input partially linear composite systems. Proceedings of the IFAC Nonlinear Control Systems Design Symposium. Bordeaux: IFAC, 1992: 379–384.
[2] T. Chen, J. Huang. Disturbance attenuation of feedforward systems with dynamic uncertainty. IEEE Transactions on Automatic Control, 2008, 53 (7): 1711–1717. · Zbl 1367.93457 · doi:10.1109/TAC.2008.929380
[3] G. Kaliora, A. Astolfi. Non-linear control of feedforward systems with bounded signals. IEEE Transactions on Automatic Control, 2004, 49(11): 1975–1990. · Zbl 1365.93447 · doi:10.1109/TAC.2004.837572
[4] P. Krishnamurthy, F. Khorrami. Generalized state scaling and applications to feedback, feedforward and nontriangular nonlinear systems. IEEE Transactions on Automatic Control, 2007, 52(1): 102–108. · Zbl 1366.93220 · doi:10.1109/TAC.2006.886534
[5] A. Teel. A nonlinear small gain theorem for analysis of control systems with saturation. IEEE Transactions on Automatic Control, 1996, 41 (9): 1256–1270. · Zbl 0863.93073 · doi:10.1109/9.536496
[6] L. Choi, T. Lim. Global exponential stabilization of a class of nonlinear systems by output feedback. IEEE Transactions on Automatic Control, 2005, 50(2): 255–257. · Zbl 1365.93439 · doi:10.1109/TAC.2004.841886
[7] C. Qian, J. Li. Global output feedback stabilization of uppertriangular nonlinear systems using a homogeneous domination approach. International Journal of Robust and Nonlinear Control, 2006, 16 (9): 441–463. · Zbl 1123.93081 · doi:10.1002/rnc.1074
[8] J. Zhai, C. Qian, M. Frye. Global finite-time stabilization via output feedback for upper-triangular systems with unknown output gain. Proceedings of IEEE Conference on Decision and Control. Atlanta: IEEE, 2010: 4096–4101.
[9] J. Zhai, C. Qian. Global control of nonlinear systems with uncertain output function using homogeneous domination approach. International Journal of Robust and Nonlinear Control, 2012, 22(14): 1543–1561. · Zbl 1274.93230 · doi:10.1002/rnc.1765
[10] J. Åström, B. Wittenmark. Computer-Controlled Systems: Theory and Design. Englewood Cliffs: Prentice-Hall, 1997.
[11] H. Khalil. Performance recovery under output feedback sampleddata stabilization of a class of nonlinear systems. IEEE Transactions on Automatic Control, 2004, 49(12): 2173–2184. · Zbl 1365.93402 · doi:10.1109/TAC.2004.838496
[12] H. Ahrens, X. Tan, H. Khalil. Multirate sampled-data output feedback control with application to smart material actuated systems. IEEE Transactions on Automatic Control, 2009, 54(11): 2518–2529. · Zbl 1367.93346 · doi:10.1109/TAC.2009.2031204
[13] D. Něsić, A. T Teel, P. Kokotović. Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations. Systems & Control Letters, 1999, 38(4/5): 259–270. · Zbl 0985.93034 · doi:10.1016/S0167-6911(99)00073-0
[14] D. Laila, D. Nesic, A. Teel. Open and closed loop dissipation inequalities under sampling and controller emulation. European Journal of Control, 2002, 8(2): 109–125. · Zbl 1293.93388 · doi:10.3166/ejc.8.109-125
[15] T. Chen, B. Francis. Input-output stability of sampled-data systems. IEEE Transactions on Automatic Control, 1991, 36(1): 50–58. · Zbl 0723.93059 · doi:10.1109/9.62267
[16] A. Dabroom, H. Khalil. Output feedback sampled-data control of nonlinear systems using high-gain observers. IEEE Transactions on Automatic Control, 2001, 46(11): 1712–1725. · Zbl 1026.93034 · doi:10.1109/9.964682
[17] D. Owen, Y. Zheng, S. Billings. Fast sampling and stability of nonlinear sampled-data systems – Part I: Existence theorems. IMA Journal of Mathematics Information, 1990, 7(1): 1–11. · Zbl 0717.93041 · doi:10.1093/imamci/7.1.1
[18] H. Du, C. Qian, S. Li. Global stabilization of a class of uncertain upper-triangular systems under sampled-data control. International Journal of Robust and Nonlinear Control, 2012, 23(6): 620–637. · Zbl 1276.93052 · doi:10.1002/rnc.2780
[19] C. Qian, H. Du. Global output feedback stabilization of a class of nonlinear systems via linear sampled-data control. IEEE Transactions on Automatic Control, 2012, 57(11): 2934–2939. · Zbl 1369.93503 · doi:10.1109/TAC.2012.2193707
[20] J. Zhai, C. Qian, H. Ye. Semiglobal output feedback stabilization of a generalized class of MIMO nonlinear systems. Journal of Dynamic Systems, Measurement and Control, 2011, 133(6): DOI 10.1115/1.400460.
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