Summary
This chapter gives an overview of the “circle-criterion” design of nonlinear observers, initiated and further developed by the author in a series of papers. It summarizes these results in a concise and unified manner and illustrates them with physically motivated design examples from fuel cell power systems, ship control, and active magnetic bearing systems.
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References
Aamo O, Arcak M, Fossen T, Kokotović P (2001) Global output tracking control of a class of Euler-Lagrange systems with monotonic nonlinearities in the velocities. International Journal of Control 74(7):649–658
Arcak M (2005) Certainty-equivalence output-feedback design with circle-criterion observers. IEEE Transactions on Automatic Control 50(6):905–909
Arcak M, Gorgun H, Pedersen L, Varigonda S (2004) A nonlinear observer design for fuel cell hydrogen estimation. IEEE Transactions on Control Systems Technology 12(1):101–110
Arcak M, Kokotović P (2001a) Nonlinear observers: A circle criterion design and robustness analysis. Automatica 37(12):1923–1930
Arcak M, Kokotović P (2001b) Observer-based control of systems with slope-restricted nonlinearities. IEEE Transactions on Automatic Control 4(7):1146–1151
Boyd S, El Ghaoui L, Feron E, Balakrishnan V (1994) Linear Matrix Inequalities in System and Control Theory, vol. 15 of SIAM Studies in Applied Mathematics. SIAM, Philadelphia, PA
Fan X, Arcak M (2003) Observer design for systems with multivariable monotone nonlinearities. Systems and Control Letters 50(4):319–330
Kazantzis N, Kravaris C (1998) Nonlinear observer design using Lyapunov’s auxiliary theorem. Systems and Control Letters 34(5):241–247
Khalil H (1999) High-gain observers in nonlinear feedback control In: Nijmeijer H, Fossen T (eds), New directions in nonlinear observer design, 249–268. Springer-Verlag, New York
Khalil H (2002) Nonlinear systems. Prentice-Hall, Upper Saddle River, NJ
Kokotović P (1992) The joy of feedback: nonlinear and adaptive. IEEE Control Systems Magazine 12:7–17
Krener A, Isidori A (1983) Linearization by output injection and nonlinear observers. Systems and Control Letters 3:47–52
Lohmiller W, Slotine JJ (1998) On contraction analysis for nonlinear systems. Automatica 34:683–696
Praly L, Arcak M (2004) A relaxed condition for stability of nonlinear observer-based controllers. Systems and Control Letters53(3–4):311–320
Raghavan S, Hedrick J (1994) Observer design for a class of nonlinear systems. International Journal of Control 59:515–528
Thau F (1973) Observing the state of non-linear dynamic systems. International Journal of Control 17:471–479
Tsiotras P, Arcak M (2005) Low-bias control of AMB subject to voltage saturation: State-feedback and observer designs. IEEE Transactions on Control Systems Technology 13(2):262–273
Zames G (1966) On the input-output stability of time-varying nonlinear feedback systems-Parts I and II. IEEE Transactions on Automatic Control 11:228–238, 465–476
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© 2006 Birkhäuser Boston
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Arcak, M. (2006). Circle-Criterion Observers and Their Feedback Applications: An Overview. In: Menini, L., Zaccarian, L., Abdallah, C.T. (eds) Current Trends in Nonlinear Systems and Control. Systems and Control: Foundations & Applications. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4470-9_1
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DOI: https://doi.org/10.1007/0-8176-4470-9_1
Publisher Name: Birkhäuser Boston
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