Linear Matrix Inequalities in Control

This chapter gives an introduction to the use of linear matrix inequalities (LMIs) in control. LMI problems are defined and tools described for transforming matrix inequality problems into a suitable LMI-format for solution. Several examples explain the use of these fundamental tools.

[1]  Paul Pinsler.  Über das Vorkommen definiter und semidefiniter Formen in Scharen quadratischer Formen , 1936 .

[2]  R. Stephenson.  A and V , 1962, The British journal of ophthalmology.

[3]  S. Kahne,et al.  Optimal control: An introduction to the theory and ITs applications , 1967, IEEE Transactions on Automatic Control.

[4]  J. Willems.  Least squares stationary optimal control and the algebraic Riccati equation , 1971 .

[5]  Huibert Kwakernaak,et al.  Linear Optimal Control Systems , 1972 .

[6]  P. Moylan,et al.  Stability criteria for large-scale systems , 1978 .

[7]  Frank L. Lewis,et al.  Optimal Control , 1986 .

[8]  P. Khargonekar,et al.  State-space solutions to standard H/sub 2/ and H/sub infinity / control problems , 1989 .

[9]  P. Gahinet,et al.  A linear matrix inequality approach to H∞ control , 1994 .

[10]  Ian Postlethwaite,et al.  Multivariable Feedback Control: Analysis and Design , 1996 .

[11]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[12]  C. Scherer.  Mixed H2/H∞ control for time‐varying and linear parametrically‐varying systems , 1996 .

[13]  Stephen P. Boyd,et al.  Semidefinite Programming , 1996, SIAM Rev..

[14]  C. Scherer,et al.  Multiobjective output-feedback control via LMI optimization , 1997, IEEE Trans. Autom. Control..

[15]  I. Postlethwaite,et al.  Accounting for uncertainty in anti-windup synthesis , 2004, Proceedings of the 2004 American Control Conference.