IEEJ Transactions on Electronics, Information and Systems
Online ISSN : 1348-8155
Print ISSN : 0385-4221
ISSN-L : 0385-4221
L2-gain Analysis and State Feedback Control Synthesis for Linear Time-Delay Systems
Infinite-Dimensional LMI Approach
Kojiro IkedaTakehito AzumaKenko Uchida
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2002 Volume 122 Issue 1 Pages 90-98

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Abstract
In this paper, we propose a new method of L2-gain analysis and state feedback control synthesis for time-delay systems via infinite-dimensional LMI, which reflects explicitly infinite-dimensionality features of time-delay systems. First, we show an infinite-dimensional LMI condition for L2-gain analysis. The infinite-dimensional LMI condition depends two parameters, and difficult to solve. Next, we propose a method of solving such infinite-dimensional LMI conditions using a convex polyhedron. The method consists of two steps: the first step is to make a convex polyhedron, and the second step is to reduce an infinite-dimensional LMI condition to a finite-dimensional LMI condition using the convex polyhedron. Finally, we discuss a state-feedback control synthesis based on the infinite-dimensional LMI conditions for L2-gain analysis and the method of solving infinite-dimensional LMIs, when the feedback gain is constrained.
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