Abstract
The purpose of this chapter is to review some notions of fundamental importance on the analysis and design of feedback laws for nonlinear control systems. The first part of the chapter begins by reviewing the notion of dynamical system and continues with a discussion of the concepts of stability and asymptotic stability of an equilibrium, with emphasis on the method of Lyapunov. Then, it continues by reviewing the notion of input-to-state stability and discussing its role in the analysis of interconnections of systems. Then, the first part is concluded by the analysis of the asymptotic behavior in the presence of persistent inputs. The second part of the chapter is devoted to the presentation of systematic methods for stabilization of relevant classes of nonlinear systems, namely, those possessing a globally defined normal form. Methods for the design of full-state feedback and, also, observer-based dynamic output feedback are presented. A nonlinear separation principle, based on the use of a high-gain observer, is discussed. A special role, in this context, is played by the methods based on feedback linearization, of which a robust version, based on the use of extended high-gain observer, is also presented.
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References
Astolfi, D., Marconi, L.: A high-gain nonlinear observer with limited gain power. IEEE Trans. Autom. Control 53(10), 2324–2334 (2016)
Birkhoff, G.D.: Dynamical Systems. American Mathematical Society, Providence (1927)
Freidovich, L.B., Khalil, H.K.: Performance recovery of feedback-linearization- based designs. IEEE Trans. Autom. Control 53, 2324–2334 (2008)
Gauthier, J.P., Kupka, I.: Deterministic Observation Theory and Applications (Cambridge University Press, Cambridge, 2001)
Hahn, W.: Stability of Motions (Springer, Berlin, 1967)
Hale, J.K., Magalhães, L.T., Oliva, W.M.: Dynamics in Infinite Dimensions. Springer, New York (2002)
Isidori, A.: Nonlinear Control Systems, 3rd edn. Springer, Berlin (1995)
Isidori, A.: Nonlinear Control Systems II. Springer, Berlin (1999)
Isidori, A., Byrnes, C.I.: Steady-state behaviors in nonlinear systems with an application to robust disturbance rejection. Ann. Rev. Control 32(1), pp. 1–16 (2007)
Jiang, Z.P., Teel, A.R., Praly, L.: Small–gain theorem for ISS systems and applications. Math. Control Signals Syst. 7, 95–120 (1994)
Khalil, H.: Nonlinear Systems, 3rd edn. Prentice Hall, Hoboken (2002)
Khalil, H.K.: High-Gain Observers in Nonlinear Feedback Control. SIAM Series: Advances in Design and Control, Philadelphia (2017)
Khalil, H.K., Esfandiari, F.: Semiglobal stabilization of a class of nonlinear systems using output feedback. IEEE Trans. Autom. Control AC-38, 1412–1415 (1993)
Liberzon, D.: Output–input stability implies feedback stabilization. Syst. Control Lett. 53, 237–248 (2004)
Sontag, E.D.: On the input–to–state stability property. Eur. J. Control. 1, 24–36 (1995)
Sontag, E.D., Wang, Y.: On characterizations of the input–to–state stability property. Syst. Contr. Lett. 24, 351–359 (1995)
Teel, A.R.: A nonlinear small gain theorem for the analysis of control systems with saturations. IEEE Trans. Autom. Control AC-41, 1256–1270 (1996)
Teel, A.R., Praly, L.: Tools for semiglobal stabilization by partial state and output feedback. SIAM J. Control. Optim. 33, 1443–1485 (1995)
Wang, L., Isidori, A., Su, H.: Global stabilization of a class of invertible MIMO nonlinear systems. IEEE Trans. Autom. Control 60(3), 616–631 (2015)
Wang, L., Isidori, A., Marconi, L., Su, H.: Stabilization by output feedback of multivariable invertible nonlinear systems. IEEE Trans. Autom. Control AC-62, 2419–2433 (2017)
Wu, Y., Isidori, A., Lu, R., Khalil, H.: Performance recovery of dynamic feedback-linearization methods for multivariable nonlinear systems. IEEE Trans. Autom. Control AC-65, 1365–1380 (2020)
Yoshizawa, T.: Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions. Springer, New York (1975)
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Isidori, A. (2023). Nonlinear Control Theory for Automation. In: Nof, S.Y. (eds) Springer Handbook of Automation. Springer Handbooks. Springer, Cham. https://doi.org/10.1007/978-3-030-96729-1_7
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DOI: https://doi.org/10.1007/978-3-030-96729-1_7
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