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

*(English)*Zbl 1265.93146Summary: 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 |

##### References:

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