Advances in Linear Matrix Inequality Methods in Control
Published on 30. September 1999
Book
Paperback/Softback
400 pages
978-0-89871-438-8 (ISBN)
Description
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.
Since the early 1990s, with the development of interior-point methods for solving LMI problems, the LMI approach has gained increased interest. One advantage of this technique is its ability to treat large classes of control problems via efficient numerical tools. This approach is widely applicable, not only in control but also in other areas where uncertainty arises. LMI techniques provide a common language for many engineering problems. Notions now popular in control, such as uncertainty and robustness, are being used in other areas through the use of LMIs. This technique is particularly attractive for industrial applications. It is well suited for the development of CAD tools that help engineers solve analysis and synthesis problems.
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.
Since the early 1990s, with the development of interior-point methods for solving LMI problems, the LMI approach has gained increased interest. One advantage of this technique is its ability to treat large classes of control problems via efficient numerical tools. This approach is widely applicable, not only in control but also in other areas where uncertainty arises. LMI techniques provide a common language for many engineering problems. Notions now popular in control, such as uncertainty and robustness, are being used in other areas through the use of LMIs. This technique is particularly attractive for industrial applications. It is well suited for the development of CAD tools that help engineers solve analysis and synthesis problems.
More details
Series
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Product notice
Paperback (trade)
Dimensions
Height: 255 mm
Width: 178 mm
Thickness: 22 mm
Weight
698 gr
ISBN-13
978-0-89871-438-8 (9780898714388)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Content
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. Joensson 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.
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. Joensson 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.