LMIs in Control/pages/LMI for convex minimization problem

LMIs in Control/pages/LMI for convex minimization problem

The System

Let $A(x)$ and $B(x)$ are matrix functions of appropriate dimensions.

Moreove, the matrix functions $A(x)$ and $B(x)$ are linear in vector $x$ where $x$ is an $m\times 1$ vector.

The Data

A convex function $f(x)$ is given and $x$ is the vector of decision variables.

The Optimization Problem

The optimization problem is to minimize the convex function $f(x)$ such that a contraint between two convex functions are satisfied for the decision variables.

The LMI: LMI for convex minimization problem

${\begin{aligned}&{\text{min}}\;\quad f(x)&\\&A(x)<B(x)\end{aligned}}$

Implementation

A link to Matlab codes for this problem in the Github repository:

External Links

A list of references documenting and validating the LMI.

• [1] - LMI in Control Systems Analysis, Design and Applications