Geodesic
Discretization schemes for Lyapunov-Krasovskii functionals in time-delay systems
Kybernetika, Tome 37 (2001) no. 4, p. [479].

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This article gives an overview of discretized Lyapunov functional methods for time-delay systems. Quadratic Lyapunov–Krasovskii functionals are discretized by choosing the kernel to be piecewise linear. As a result, the stability conditions may be written in the form of linear matrix inequalities. Conservatism may be reduced by choosing a finer mesh. Simplification techniques, including elimination of variables and using integral inequalities are also discussed. Systems with multiple delays and distributed delays are also treated. Finally, the treatment of uncertainties and input-output performance requirements are discussed.
Classification : 93B40, 93C23, 93C55, 93D05, 93D09
Keywords: time-delay system; Lyapunov-Krasovskii functional; multiple delays 
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     author = {Gu, Keqin},
     title = {Discretization schemes for {Lyapunov-Krasovskii} functionals in time-delay systems},
     journal = {Kybernetika},
     pages = {[479]},
     publisher = {mathdoc},
     volume = {37},
     number = {4},
     year = {2001},
     mrnumber = {1859097},
     zbl = {1265.93176},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2001__37_4_a5/}
}
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Gu, Keqin. Discretization schemes for Lyapunov-Krasovskii functionals in time-delay systems. Kybernetika, Tome 37 (2001) no. 4, p. [479]. http://geodesic.mathdoc.fr/item/KYB_2001__37_4_a5/