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Linear output feedback with dynamic high gain for nonlinear systems. (English) Zbl 1157.93494
Summary: We propose a linear output feedback with dynamic high gain for global regulation of a class of nonlinear systems. The uncertain nonlinearities are assumed to be bounded by a polynomial function of the output multiplied by unmeasured states. The crucial point made in this paper is that a linear observer-based output feedback can globally regulate an equilibrium of strongly nonlinear systems, provided that a single high gain is appropriately tuned.

93D15 Stabilization of systems by feedback
93C15 Control/observation systems governed by ordinary differential equations
93D25 Input-output approaches in control theory
Full Text: DOI
[1] Jiang, Z.P.; Mareels, I., Robust nonlinear integral control, IEEE trans. automat. control, 46, 8, 1336-1342, (2001) · Zbl 1002.93055
[2] Jiang, Z.P.; Mareels, I.; Wang, Y., A Lyapunov formulation of the nonlinear small gain theorem for interconnected ISS systems, Automatica, 32, 8, 1211-1215, (1996) · Zbl 0857.93089
[3] Jiang, Z.P.; Teel, A.R.; Praly, L., Small-gain theorem for ISS systems and applications, Math. control, signals and systems, 7, 95-120, (1994) · Zbl 0836.93054
[4] Khalil, H.; Saberi, A., Adaptive stabilization of a class of nonlinear systems using high-gain feedback, IEEE trans. automat. control, 32, 11, 1031-1035, (1987) · Zbl 0625.93040
[5] P. Krishnamurthy, F. Khorrami, Generalized adaptive output-feedback form with unknown parameters multiplying high output relative-degree states, Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, NV, December 2002, pp. 1503-1508.
[6] Krstić, M.; Kanellakopoulos, I.; Kokotović, P.V., Nonlinear and adaptive control design, (1995), Wiley New York · Zbl 0763.93043
[7] Marino, R.; Tomei, P., Nonlinear control design: geometric, adaptive and robust, (1995), Prentice-Hall London · Zbl 0833.93003
[8] Mazenc, F.; Praly, L.; Dayawansa, W.P., Global stabilization by output feedback: examples and counterexamples, Systems control lett., 23, 119-125, (1994) · Zbl 0816.93068
[9] L. Praly, Generalized weighted homogeneity and state dependent time scale for linear controllable systems, Proceedings of the 36th IEEE Conference on Decision and Control, December 1997, pp. 4342-4347.
[10] Praly, L., Asymptotic stabilization via output feedback for lower triangular systems with output dependent incremental rate, IEEE trans. automat. control, 48, 6, 1103-1108, (2003) · Zbl 1364.93718
[11] Praly, L.; Jiang, Z.P., Stabilization by output feedback for systems with ISS inverse dynamics, Systems control lett., 21, 19-33, (1993) · Zbl 0784.93088
[12] Praly, L.; Wang, Y., Stabilization in spite of matched unmodeled dynamics and an equivalent definition of input-to-state stability, Math. control, signals, systems, 9, 1-33, (1996) · Zbl 0869.93040
[13] C. Qian, W. Lin, Universal stabilization of a class of nonlinear systems by output feedback, Proc. American Control Conference, Anchorage, AK, May 8-10, 2002, pp. 122-127.
[14] Sontag, E.; Wang, Y., On characterizations of the input-to-state stability property, Systems control lett., 24, 351-359, (1995) · Zbl 0877.93121
[15] Spooner, J.T.; Maggiore, M.; Ordonez, R.; Passino, K.M., Stable adaptive control and estimation for nonlinear systems, (2002), Wiley New York
[16] Szarski, J., Differential inequalities, (1965), PWN Warsaw · Zbl 0135.25804
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