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Infinite-dimensional LMI approach to analysis and synthesis for linear time-delay systems. (English) Zbl 1265.93146
Summary: 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. Firstly, 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 infinite dimensionality of the LMIs makes the result difficult to apply. Secondly, 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.

##### MSC:
 93C23 Control/observation systems governed by functional-differential equations 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 93B50 Synthesis problems
##### Keywords:
time-delay system; linear system; LMI
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##### References:
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