Abstract
This chapter is devoted to the study of systems described by Integral Delay Equations (IDEs). Systems described by IDEs arise when predictor feedback is used for the stabilization of finite-dimensional control systems with input delays; this fact was pointed out in Chapter 1. The direct implementation of the predictor feedback itself is a system described by IDEs: this is one of the viewpoints of describing the dynamics of the closed-loop system under predictor feedback.
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References
Karafyllis, I., Jiang, Z.-P.: Stability and Stabilization of Nonlinear Systems. Communications and Control Engineering. Springer, London (2011)
Angeli, D., Sontag, E.D.: Forward completeness, unbounded observability and their Lyapunov characterizations. Syst. Control Lett. 38(4–5), 209–217 (1999)
Teel, A.R.: Connections between Razumikhin-type theorems and the ISS nonlinear small gain theorem. IEEE Trans. Autom. Control 43(7), 960–964 (1998)
Hale, J.K., Lunel, S.M.V.: Introduction to Functional Differential Equations. Springer, New York (1993)
Sontag, E.D.: Smooth stabilization implies coprime factorization. IEEE Trans. Autom. Control 34, 435–443 (1989)
Fillipov, A.V.: Differential Equations with Discontinuous Right-Hand Sides. Kluwer Academic Publishers, Dordrecht (1988)
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Karafyllis, I., Krstic, M. (2017). Systems Described by Integral Delay Equations. In: Predictor Feedback for Delay Systems: Implementations and Approximations. Systems & Control: Foundations & Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-42378-4_7
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DOI: https://doi.org/10.1007/978-3-319-42378-4_7
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Publisher Name: Birkhäuser, Cham
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Online ISBN: 978-3-319-42378-4
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