LMIs in Control/Minimum-Rank Solutions of Linear Matrix Equations/Low-Dimensional Euclidean Embedding Problem

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LMIs in Control/Minimum-Rank Solutions of Linear Matrix Equations/Low-Dimensional Euclidean Embedding Problem

This is a Template for Creating An LMI Page

The System

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

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.

$\begin{array}{cc}\text{Find}X:& \\ \left[\begin{array}{c}X\end{array}\right]& >0\\ \left[\begin{array}{c}{A}^{T}X+XA\end{array}\right]& <0\end{array}$

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.