LMIs in Control/Minimum-Rank Solutions of Linear Matrix Equations/Minimum-Order Linear System Realization via minimizing the rank of the Hankel matrix

WIP

This is a Template for Creating An LMI Page

The System


\begin{align} \dot x(t)&=Ax(t)\\ x(0)&=x_0 \end{align}$$

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.



\begin{align} \text{Find} \; X:&\\ \begin{bmatrix} X\end{bmatrix}&>0\\ \begin{bmatrix} A^T X+XA\end{bmatrix}&<0 \end{align}$$

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