By Laurent El Ghaoui, Silviu-Iulian Niculescu
Linear matrix inequalities (LMIs) have lately emerged as valuable instruments for fixing a few keep watch over difficulties. This publication offers an up to date account of the LMI approach and covers themes comparable to fresh LMI algorithms, research and synthesis matters, nonconvex difficulties, and purposes. It additionally emphasizes functions of the strategy to components except keep watch over. the fundamental thought of the LMI process on top of things is to approximate a given keep watch over challenge through an optimization challenge with linear goal and so-called LMI constraints. The LMI process ends up in a good numerical resolution and is especially suited for issues of doubtful facts and a number of (possibly conflicting) standards.
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Additional info for Advances in Linear Matrix Inequality Methods in Control (Advances in Design and Control)
Part I Introduction This page intentionally left blank Chapter 1 Robust Decision Problems in Engineering: A Linear Matrix Inequality Approach L. -I. 1 Basic idea The basic idea of the LMI method is to formulate a given problem as an optimization problem with linear objective and linear matrix inequality (LMI) constraints. An LMI constraint on a vector x e Rm is one of the form where the symmetric matrices Fj = F? G R JVxJV , i = 0,... ,m, are given. The minimization problem where c € R m , and F > 0 means the matrix F is symmetric and positive semidefinite, is called a semidefinite program (SDP).
Edu/"boyd/group_index. 6. Illustrations in control 25 and later by Commeau, is an interface to the codes SP, SDPpack, and SDPHA. http : //www . ensta . f r/~gropco/ • The code SDPpack, outlined in Chapter 3 of this book, implements a primal-dual algorithm due to Alizadeh, Haeberly, and Overton  and Alizadeh et al. . http : //www . cs . nyu . edu/cs/f aculty/overton/sdppack/sdppack . html • The code SDPA: developed by Fujisawa, Kojima, and Nakata; the underlying algorithm is described in .
This offers a drastic advantage over design methods that rely on a single criterion deemed to reflect all design constraints; the choice of a relevant criterium is sometimes a nontrivial task. Wide applicability. The techniques used in the approach are relevant far beyond control and estimation. This opens exciting avenues of research where seemingly very different problems are analyzed and solved in a unified framework. For example, the method known in LMI-based control as the S-procedure can be successfully applied in combinatorial optimization, leading to efficient relaxations of hard problems.