Advances in Linear Matrix Inequality Methods in Control by Laurent El Ghaoui, Silviu-Iulian Niculescu

By Laurent El Ghaoui, Silviu-Iulian Niculescu

Linear matrix inequalities (LMIs) have lately emerged as important instruments for fixing a few keep watch over difficulties. This e-book presents an up to date account of the LMI strategy and covers themes comparable to contemporary LMI algorithms, research and synthesis concerns, nonconvex difficulties, and functions. It additionally emphasizes functions of the strategy to components except regulate. the elemental thought of the LMI procedure up to the mark is to approximate a given keep an eye on challenge through an optimization challenge with linear goal and so-called LMI constraints. The LMI procedure ends up in an effective numerical answer and is very fitted to issues of doubtful information and a number of (possibly conflicting) standards.

Show description

Read Online or Download Advances in Linear Matrix Inequality Methods in Control (Advances in Design and Control) PDF

Best linear programming books

Operations Research Proceedings 2004: Selected Papers of the Annual International Conference of the German Operations Research Society (GOR) - Jointly ... Research (NGB), Tilburg, September 1-3, 2004

Those complaints supply details at the latest advances in operations study and comparable components in economics, arithmetic, and desktop technology, contributed by way of lecturers and practitioners from around the globe.

Nonlinear Equations and Optimisation, Volume 4 (Numerical Analysis 2000)

/homepage/sac/cam/na2000/index. html7-Volume Set now to be had at certain set rate ! in a single of the papers during this assortment, the comment that "nothing in any respect occurs within the universe during which a few rule of extreme of minimal doesn't seem" is attributed to no much less an expert than Euler. Simplifying the syntax a bit, we'd paraphrase this as every little thing is an optimization challenge.

Advanced Linear Models: Theory and Applications (Statistics: A Series of Textbooks and Monographs)

This paintings info the statistical inference of linear types together with parameter estimation, speculation checking out, self assurance durations, and prediction. The authors speak about the appliance of statistical theories and methodologies to varied linear types corresponding to the linear regression version, the research of variance version, the research of covariance version, and the variance elements version.

Mathematical Analysis and Numerical Methods for Science and Technology: Volume 2 Functional and Variational Methods

Those 6 volumes - the results of a ten yr collaboration among the authors, of France's prime scientists and either individual foreign figures - collect the mathematical wisdom required through researchers in mechanics, physics, engineering, chemistry and different branches of program of arithmetic for the theoretical and numerical answer of actual versions on desktops.

Additional resources for Advances in Linear Matrix Inequality Methods in Control (Advances in Design and Control)

Sample text

Checking if a given candidate solution x is robustly feasible is already very difficult in general. Our objective is to find lower bounds on this problem in the form of SDP. 4. 24). The variables in this SDP are x (the original decision variable) and 5 (the "multiplier" matrix). 14)), the approximation is exact. 16 El Ghaoui and Niculescu A special case: Robust linear programming (LP) Consider the LP Assume that the a^'s and 6i's are subject to unstructured perturbations. , L, and p > 0 is a given measure of the perturbation level.

The corresponding characterization is Euclidean-norm bounds. } 2 The above representation is usually referred to as the "linear-fractional transformation" (LFT) [446]. We believe the term representation is more appropriate here. 3. Uncertainty models 11 Maximum-norm bounds. ) Sector bounds. Assume A = {s • I \ s G C, characterization is s + s* > 0}. The corresponding Of course, it is possible to mix different bounds to cover more complicated cases. 2 Operator point of view The above uncertainty models for data matrices can be interpreted as input-output maps, as follows.

18 El Ghaoui and Niculescu Robust synthesis We now seek a sufficient condition, A being fixed, so that holds. Now x becomes a variable. Due to possible cross products between x and P in the previous sufficient condition, the problem is not convex, contrary to what happens in the robust SDP case. 27) is true if and only if the optimum is A 2 n. 5). In general, the above problem is not convex; however, several efficient techniques can be used (see Part V). One of these techniques, described in Chapters 16 and 17, relies on a simple linearization of the quadratic objective and leads to a sequence of SDPs.

Download PDF sample

Rated 4.50 of 5 – based on 12 votes