LMIs in Control/Matrix and LMI Properties and Tools/Continuous Time/Structured Singular Value
The LMI can be used to find a Θ {\displaystyle \Theta } that belongs to the set of scalings P Θ {\displaystyle P\Theta } . Minimizing γ {\displaystyle \gamma } allows to minimize the squared norm of Θ M Θ − 1 {\displaystyle \Theta M\Theta ^{-}1} .
The matrices A ∈ R n × n , B ∈ R n × m , C ∈ R o × n , D ∈ R o × m {\displaystyle A\in R^{n\times n},B\in R^{n\times m},C\in R^{o\times n},D\in R^{o\times m}} .
There exists Θ ∈ Θ such that | | Θ M Θ − 1 | | 2 < γ . {\displaystyle {\begin{aligned}{\text{There exists }}\Theta \in \Theta {\text{ such that }}||\Theta M\Theta ^{-1}||^{2}<\gamma .\end{aligned}}}
The optimization problem and the LMI are equivalent. γ must be optimized using bisection. {\displaystyle {\text{The optimization problem and the LMI are equivalent. }}\gamma {\text{ must be optimized using bisection.}}}
https://github.com/mcavorsi/LMI
Eigenvalue Problem
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