Infinite-dimensional LMI approach to analysis and synthesis for linear time-delay systems

Ikeda, Kojiro ; Azuma, Takehito ; Uchida, Kenko

Kybernetika, Tome 37 (2001) no. 4, pp. 505-520

Abstract (VO)

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.

Détail

Classification : 93B50, 93B51, 93C23, 93D05
Keywords: time-delay system; linear system; LMI

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