Linear matrix inequalities (LMIs) have recently emerged as useful tools for solving a number of control problems. This book provides an up-to-date account of the LMI method and covers topics such as recent LMI algorithms, analysis and synthesis issues, nonconvex problems, and applications. It also emphasizes applications of the method to areas other than control. The basic idea of the LMI method in control is to approximate a given control problem via an optimization problem with linear objective and so-called LMI constraints. The LMI method leads to an efficient numerical solution and is particularly suited to problems with uncertain data and multiple (possibly conflicting) specifications.
Preface; Notation; Part I. Introduction. Robust Decision Problems in Engineering: A linear matrix inequality approach L. El Ghaoui and S.-I. Niculescu; Part II. Algorithms and Software: Mixed Semidefinite-Quadratic-Linear Programs J.-P. A. Haeberly, M. V. Nayakkankuppam and M. L. Overton; Nonsmooth algorithms to solve semidefinite programs C. Lemarechal and F. Oustry; sdpsol: A Parser/Solver for Semidefinite Programs with Matrix Structure S.-P. Wu and S. Boyd; Part III. Analysis: Parametric Lyapunov Functions for Uncertain Systems: The Multiplier Approach M. Fu and S. Dasgupta; Optimization of Integral Quadratic Constraints U. Jonsson and A. Rantzer; Linear Matrix Inequality Methods for Robust H2 Analysis: A Survey with Comparisons F. Paganini and E. Feron; Part IV. Synthesis. Robust H2 Control K. Y. Yang, S. R. Hall and E. Feron; Linear Matrix Inequality Approach to the Design of Robust H2 Filters C. E. de Souza and A. Trofino; Robust Mixed Control and Linear Parameter-Varying Control with Full Block Scalings C. W. Scherer; Advanced Gain-Scheduling Techniques for Uncertain Systems P. Apkarian and R. J. Adams; Control Synthesis for Well-Posedness of Feedback Systems T. Iwasaki; Part V. Nonconvex Problems. Alternating Projection Algorithms for Linear Matrix Inequalities Problems with Rank Constraints K. M. Grigoriadis and E. B. Beran; Bilinearity and Complementarity in Robust Control M. Mesbahi, M. G. Safonov and G. P. Papavassilopoulos; Part VI. Applications:Linear Controller Design for the NEC Laser Bonder via Linear Matrix Inequality Optimization J. Oishi and V. Balakrishnan; Multiobjective Robust Control Toolbox for LMI-Based Control S. Dussy; Multiobjective Control for Robot Telemanipulators J. P. Folcher and C. Andriot; Bibliography; Index.
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