LMIs in Control/Tools/Basic Matrix Theory
Basic Matrix Notation
Consider the complex matrix .
Transpose of a Matrix
The transpose of , denoted as or is:
Adjoint of a Matrix
The adjoint or hermitian conjugate of , denoted as is:
Where is the complex conjugate of matrix element .
Notice that for a real matrix , .
Important Properties of Matricies
Hermitian, Self-Adjoint, and Symmetric Matricies
A square matrix is called Hermitian or self-adjoint if .
If is Hermitian then it is called symmetric.
A square matrix is called unitary if or .
WIP, additional references to be added
- 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.