[<< wikibooks] LMIs in Control/Minimum-Rank Solutions of Linear Matrix Equations/Low-Rank Matrix Completion

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LMIs in Control/Minimum-Rank Solutions of Linear Matrix Equations/Low-Rank Matrix Completion
This is a Template for Creating An LMI Page
== The System ==
x
˙
(
t
)
=
A
x
(
t
)
x
(
0
)
=
x
0
{\displaystyle {\begin{aligned}{\dot {x}}(t)&=Ax(t)\\x(0)&=x_{0}\end{aligned}}}
== The Data ==
A List of inputs needed for the problem to be well-defined.
== The Optimization Problem ==
A description of the Problem to be solved, if appropriate.
== The LMI: The Lyapunov Inequality ==
Title and mathematical description of the LMI formulation.
Find
X
:
[
X
]
>
0
[
A
T
X
+
X
A
]
<
0
{\displaystyle {\begin{aligned}{\text{Find}}\;X:&\\{\begin{bmatrix}X\end{bmatrix}}&>0\\{\begin{bmatrix}A^{T}X+XA\end{bmatrix}}&<0\end{aligned}}}
== Conclusion: ==
Interpretation of the results of the LMI
== Implementation ==
A link to CodeOcean or other online implementation of the LMI
== Related LMIs ==
Links to other closely-related LMIs
== External Links ==
A list of references documenting and validating the LMI.
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.
== Return to Main Page: ==