LMIs in Control/Click here to continue/Fundamentals of Matrix and LMIs/Minimizing Norm by Scaling
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Minimizing Norm by Scaling[edit | edit source]
There are many cases in which a norm should be minimized, such as in applications of the or norm optimal control.
The System[edit | edit source]
is a matrix . is some diagonal, nonsingular .
The Data[edit | edit source]
The optimal diagonally scaled norm of a matrix is defined as , where is diagonal and nonsingular.
The LMI:Minimizing Norm by Scaling[edit | edit source]
Therefore, is the optimal value of the generalized eigenvalue problem
minimize
subject to and diagonal,
Conclusion:[edit | edit source]
This result can be extended in many ways, such as in applications of or optimal control.
Implementation[edit | edit source]
This implementation requires Yalmip and Sedumi.
Related LMIs[edit | edit source]
External Links[edit | edit source]
- LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
- LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.
- LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.
- LMIs in Control Systems: Analysis, Design and Applications - by Guang-Ren Duan and Hai-Hua Yu, CRC Press, Taylor & amp; Francis Group, 2013.
Return to Main Page:[edit | edit source]
LMIs in Control: https://en.wikibooks.org/wiki/LMIs_in_Control