LMIs in Control/Linear matrix inequalities and control theory/pages/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. Unitary Matricies A square matrix is called unitary if or . External Links 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.