LMIs in Control/Tools/Eigenvalue Problem

The System


\begin{align} \dot x(t)&=Ax(t)+Bu(t), \\ y(t) &= Cx(t) \end{align}$$

The Data
The matrices $$ A,B,C $$.

The Optimization Problem
$$ \text{ Minimize } \gamma \text{ subject to the LMI below.} $$

The LMI: The Lyapunov Inequality


\begin{align} \text{Find} \; &P>0:\\ \begin{bmatrix} -A^TP-PA-C^TC & PB \\ B^TP & \gamma I\end{bmatrix} > 0\\ \end{align}$$

Conclusion:
The eigenvalue problem can be utilized to minimize the maximum eigenvalue of a matrix that depends affinely on a variable.

Implementation
https://github.com/mcavorsi/LMI

Related LMIs
Structured Singular Value