# LMIs in Control/Minimum-Rank Solutions of Linear Matrix Equations/Low-Rank Parametrization

WIP

LMIs in Control/Minimum-Rank Solutions of Linear Matrix Equations/Low-Rank Parametrization

This is a Template for Creating An LMI Page

## The System

{\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.

{\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