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