Geodesic
Nonlinear bounded control for time-delay systems
Kybernetika, Tome 37 (2001) no. 4, p. [381]

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A method to derive a nonlinear bounded state feedback controller for a linear continuous-time system with time-delay in the state is proposed. The controllers are based on an $e$-parameterized family of algebraic Riccati equations or on an $e$-parameterized family of LMI optimization problems. Hence, nested ellipsoidal neighborhoods of the origin are determined. Thus, from the Lyapunov–Krasovskii theorem, the uniform asymptotic stability of the closed-loop system is guaranteed and a certain performance level is attained through a quadratic cost function.
Classification : 93B52, 93C10, 93C23, 93D20
Keywords: state feedback controller; time-delay 
@article{KYB_2001__37_4_a1,
     author = {Garcia, Germain and Tarbouriech, Sophie},
     title = {Nonlinear bounded control for time-delay systems},
     journal = {Kybernetika},
     pages = {[381]},
     publisher = {mathdoc},
     volume = {37},
     number = {4},
     year = {2001},
     mrnumber = {1859093},
     zbl = {1265.93131},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2001__37_4_a1/}
}
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Garcia, Germain; Tarbouriech, Sophie. Nonlinear bounded control for time-delay systems. Kybernetika, Tome 37 (2001) no. 4, p. [381]. http://geodesic.mathdoc.fr/item/KYB_2001__37_4_a1/