By Alexandre Seuret, Laurentiu Hetel, Jamal Daafouz, Karl H. Johansson
This edited monograph contains state of the art contributions on non-stop time dynamical networks with delays. The booklet is split into 4 elements. the 1st half provides instruments and strategies for the research of time-delay platforms with a selected awareness on keep an eye on difficulties of enormous scale or infinite-dimensional platforms with delays. the second one a part of the booklet is devoted to using time-delay versions for the research and layout of Networked keep an eye on platforms. The 3rd a part of the booklet specializes in the research and layout of platforms with asynchronous sampling durations which happen in Networked regulate platforms. The final a part of the booklet exposes a number of contributions facing the layout of cooperative keep watch over and remark legislation for networked keep an eye on platforms. the objective viewers basically includes researchers and specialists within the box of regulate conception, however the e-book can also be important for graduate scholars.
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1) with the state-feedback u(t) = F x(t − r ). 40) is x(t) = (A + B F)x(t − r ), t ≥ 0. 41). 1) is useful for performance analysis. 43) with the controlled output equation y(t) = C x(t) + Du(t). 44) The input w(t) is a disturbance, and is assumed to be in L 2 ([0, ∞), Rw ), while the matrices E, C and D are real with appropriate size. 46) for a given γ ≥ 0. This problem admits an immediate answer. Theorem 3 Assume that there exist a symmetric positive definite matrix P and a matrix Y such that the matrix ⎤ ⎡ P 0 (A P + BY )T (C(A P + BY ) + DY )T ⎥ ⎢∗ γ2 · I ET (C E)T ⎥ M =⎢ ⎦ ⎣∗ ∗ P 0 ∗ ∗ ∗ I is positive definite.