Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Linear Matrix Inequality Techniques in Optimal Control

  • Robert E. SkeltonEmail author
Living reference work entry

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DOI: https://doi.org/10.1007/978-1-4471-5102-9_207-2

Abstract

LMI (linear matrix inequality) techniques offer more flexibility in the design of dynamic linear systems than techniques that minimize a scalar functional for optimization. For linear state space models, multiple goals (performance bounds) can be characterized in terms of LMIs, and these can serve as the basis for controller optimization via finite-dimensional convex feasibility problems. LMI formulations of various standard control problems are described in this entry, including dynamic feedback stabilization, covariance control, LQR, H control, and L control. The integration of control and information architecture design (i.e., adding sensor/actuator precision selection to the control problem) is also shown to be a convex problem by formulating the feasibility constraints as LMIs.

Keywords

Control system design Covariance control H control L control LQR/LQG Matrix inequalities Sensor/actuator design Integrated plant and control design 
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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2020

Authors and Affiliations

  1. 1.Texas A&M UniversityCollege StationUSA

Section editors and affiliations

  • Michael Cantoni
    • 1
  1. 1.Department of Electrical & Electronic EngineeringThe University of MelbourneParkvilleAustralia