# LMIs in Control/pages/Nonconvex Multi-Criterion Quadratic Problems

LMIs in Control/pages/Nonconvex Multi-Criterion Quadratic Problems

This is a WIP based on the template

## The System

The system for this LMI is a linear time invariant system that can be represented in state space as shown below:

{\displaystyle {\begin{aligned}{\dot {x}}&=Ax+Bw,x(0)=x_{0}\\y&=Cx\\\end{aligned}}}

where the system is assumed to be controllable.

## The Data

The matrices ${\displaystyle A,B,C}$.

## The Optimization Problem

The following feasibility problem should be solved: Find

## The LMI: The Lyapunov Inequality

Title and mathematical description of the LMI formulation.

{\displaystyle {\begin{aligned}{\text{Find}}\;&P>0,\Lambda =diag(\lambda _{1},\dots ,\lambda _{n_{p}}),T=diag(\tau _{1}):\\{\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