Advances in linear matrix inequality methods in control by Laurent El Ghaoui, Silviu-Iulian Niculescu PDF

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By Laurent El Ghaoui, Silviu-Iulian Niculescu

ISBN-10: 0898714389

ISBN-13: 9780898714388

Linear matrix inequalities (LMIs) have lately emerged as invaluable instruments for fixing a couple of keep watch over difficulties. This ebook presents an up to date account of the LMI technique and covers subject matters reminiscent of fresh LMI algorithms, research and synthesis concerns, nonconvex difficulties, and functions. It additionally emphasizes functions of the strategy to components except keep an eye on.

The simple suggestion of the LMI technique up to the mark is to approximate a given keep an eye on challenge through an optimization challenge with linear aim and so-called LMI constraints. The LMI process ends up in an effective numerical resolution and is especially suited for difficulties with doubtful info and a number of (possibly conflicting) necessities.

Since the early Nineteen Nineties, with the improvement of interior-point tools for fixing LMI difficulties, the LMI procedure has received elevated curiosity. One benefit of this method is its skill to deal with huge sessions of keep an eye on difficulties through effective numerical instruments. This strategy is broadly appropriate, not just on top of things yet additionally in different parts the place uncertainty arises. LMI concepts offer a universal language for lots of engineering difficulties. Notions now renowned in keep an eye on, equivalent to uncertainty and robustness, are getting used in different components by using LMIs. this system is especially beautiful for commercial functions. it truly is well matched for the improvement of CAD instruments that aid engineers resolve research and synthesis difficulties.

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Download e-book for kindle: Advances in linear matrix inequality methods in control by Laurent El Ghaoui, Silviu-Iulian Niculescu

Linear matrix inequalities (LMIs) have lately emerged as beneficial instruments for fixing a few regulate difficulties. This e-book presents an updated account of the LMI strategy and covers themes comparable to contemporary LMI algorithms, research and synthesis matters, nonconvex difficulties, and purposes. It additionally emphasizes purposes of the tactic to components except keep watch over.

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Mixed parameter- scheduled/robust problems. In some problems, the decision vector is a mixture of a set of real variables and of functions of some parameters. In control, this kind of problem occurs when only some parameters are available for measurement. 1 We take the uncertainty to be a matrix instead of a vector for reasons to be made clear later. 2. Decision problems with uncertain data 7 In control theory, we interpret the above problems as robust multispecification control problems, where several (possibly conflicting) constraints have to be satisfied in a robust manner.

In a first step, we "forget" uncertainty and apply Lagrange relaxation to the "frozen" system. This results in a sufficient condition for stability: There exists a matrix 5 such that This condition is known as a quadratic stability condition, since it requires the existence of a quadratic Lyapunov function proving stability of the uncertain system. In general, the above condition is still not tractable, despite the fact it is a convex condition on S. However, the relaxed problem above now belongs to the realm of robust SDP.

Every (matrix-valued) rational function M(<5) of 6 € Rp that is well defined for 6 = 0 admits an LFR of the form valid for whenever det(/ — DA) ^ 0 for appropriate matrices M, L, R, D and integers We note that, when I = 1 (that is, for a monovariable rational matrix function), the matrices M, L, R, D are simply a state-space realization of the transfer matrix M+L(sI— D)~1R, where s = 1/6. An LFR of M can then always be constructed in a "minimal" way, such that the size of matrix A is exactly the order of M in s.

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Advances in linear matrix inequality methods in control by Laurent El Ghaoui, Silviu-Iulian Niculescu


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