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

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

This is a Template for Creating An LMI Page

The System

${\begin{aligned}{\dot {x}}(t)&=Ax(t)\\x(0)&=x_{0}\end{aligned}}$

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.

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

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.