Algorithms and software for LMI problems in control

@article{Vandenberghe1997AlgorithmsAS,
  title={Algorithms and software for LMI problems in control},
  author={Lieven Vandenberghe and Venkataramanan Balakrishnan},
  journal={IEEE Control Systems Magazine},
  year={1997},
  volume={17},
  pages={89-95}
}
A number of important problems from system and control theory can be numerically solved by reformulating them as convex optimization problems with linear matrix inequality (LMI) constraints. While numerous articles have appeared cataloging applications of LMIs to control system analysis and design, there have been few publications in the control literature describing the numerical solution of these optimization problems. The purpose of this article is to provide an overview of the state of the… 

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TLDR
The Projective Method is described, a complexity analysis is provided, and applications to two generic LMI problems (feasibility and linear objective minimization) are discussed.

Algorithms and software tools for LMI problems in control: an overview

  • L. VandenbergheV. Balakrishnan
  • Mathematics, Computer Science
    Proceedings of Joint Conference on Control Applications Intelligent Control and Computer Aided Control System Design
  • 1996
TLDR
An overview of recent developments in algorithms and software for linear matrix inequality (LMI) problems and some extensions of the semidefinite programming (SDP) problem are given.

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