Geodesic
Infinite-dimensional LMI approach to analysis and synthesis for linear time-delay systems
Kybernetika, Tome 37 (2001) no. 4, p. [505]

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This paper considers an analysis and synthesis problem of controllers for linear time-delay systems in the form of delay-dependent memory state feedback, and develops an Linear Matrix Inequality (LMI) approach. First, we present an existence condition and an explicit formula of controllers, which guarantee a prescribed level of $L^2$ gain of closed loop systems, in terms of infinite-dimensional LMIs. This result is rather general in the sense that it covers, as special cases, some known results for the cases of delay- independent/dependent and memoryless/memory controllers, while the infinity dimensionality of the LMIs makes the result difficult to apply. Second, we introduce a technique to reduce the infinite-dimensional LMIs to a finite number of LMIs, and present a feasible algorithm for synthesis of controllers based on the finite-dimensional LMIs.
Classification : 93B50, 93B51, 93C23, 93D05
Keywords: time-delay system; linear system; LMI 
@article{KYB_2001__37_4_a6,
     author = {Ikeda, Kojiro and Azuma, Takehito and Uchida, Kenko},
     title = {Infinite-dimensional {LMI} approach to analysis and synthesis for linear time-delay systems},
     journal = {Kybernetika},
     pages = {[505]},
     publisher = {mathdoc},
     volume = {37},
     number = {4},
     year = {2001},
     mrnumber = {1859098},
     zbl = {1265.93146},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2001__37_4_a6/}
}
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Ikeda, Kojiro; Azuma, Takehito; Uchida, Kenko. Infinite-dimensional LMI approach to analysis and synthesis for linear time-delay systems. Kybernetika, Tome 37 (2001) no. 4, p. [505]. http://geodesic.mathdoc.fr/item/KYB_2001__37_4_a6/