Abstract
We studied internal stabilization of linear systems subject to actuator magnitude saturation in Chap. 4, and the same in Chap. 6, however, when the actuator is subject to both magnitude and rate saturation. The block diagram of Fig. 10.1 depicts the setup. Although such actuator saturation occurs ubiquitously, in this chapter we consider a broader class of nonlinear systems than that depicted in Fig. 10.1. As pointed out in Chap. 1, an important and common paradigm of nonlinear systems is that they are indeed linear systems in which nonlinear elements are sandwiched or embedded as shown in Fig. 10.2. A model of a common nonlinear element is a static nonlinearity followed by a linear system or vice-versa. In either case, the block diagram of Fig. 10.2 depicts a commonly prevailing situation besides linear systems subject to merely actuator saturation.
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References
Z. Lin and A. Saberi, “A low-and-high gain approach to semi-global stabilization and/or semi-global practical stabilization of a class of linear systems subject to input saturation via linear state and output feedback”, in Proc. 32nd CDC, San Antonio, TX, 1993, pp. 1820–1821.
________, “Semi-global exponential stabilization of linear discrete-time systems subject to ‘input saturation’ via linear feedbacks”, Syst. & Contr. Letters, 24(2), 1995, pp. 125–132.
A. Megretski, “L 2 BIBO output feedback stabilization with saturated control”, in Proc. 13th IFAC world congress, vol. D, San Francisco, 1996, pp. 435–440.
A. Saberi, P.V. Kokotovic, and H.J. Sussmann, “Global stabilization of partially linear composite systems”, SIAM J. Contr. & Opt., 28(6), 1990, pp. 1491–1503.
P. Seibert and R. Suarez, “Global stabilization of nonlinear cascade systems”, Syst. & Contr. Letters, 14(4), 1990, pp. 347–352.
________, “Global stabilization of a certain class of nonlinear systems”, Syst. & Contr. Letters, 16(1), 1991, pp. 17–23.
A.A. Stoorvogel, X. Wang, A. Saberi, and P. Sannuti, “Stabilization of sandwich non-linear systems with low-and-high gain feedback design”, in American Control Conference, Baltimore, MD, 2010, pp. 4217–4222.
A. Taware and G. Tao, “Neural-hybrid control of systems with sandwiched dead-zones”, Int. J. Adapt. Contr. and Sign. Proc., 16(7), 2002, pp. 473–496.
A. Taware, G. Tao, and C. Teolis, “Design and analysis of a hybrid control scheme for sandwich nonsmooth nonlinear systems”, IEEE Trans. Aut. Contr., 47(1), 2002, pp. 145–150.
X. Wang, A.A. Stoorvogel, A. Saberi, H.F. Grip, S. Roy, and P. Sannuti, “Stabilization of a class of nonlinear sandwich systems via state feedback”, IEEE Trans. Aut. Contr., 55(9), 2010, pp. 2156–2160.
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Saberi, A., Stoorvogel, A.A., Sannuti, P. (2012). Sandwich systems: state feedback. In: Internal and External Stabilization of Linear Systems with Constraints. Systems & Control: Foundations & Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4787-2_10
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