Linear Matrix Inequalities (LMI)

Linear Matrix Inequalities (LMIs) are mathematical expressions involving matrices that set certain conditions—like bounds or stability criteria—using linear functions of the matrix entries. They are used to formulate and solve complex optimization problems in control theory, signal processing, and engineering. LMIs are valuable because they can be efficiently checked and solved with specialized algorithms, making it easier to ensure systems behave safely and reliably within desired parameters. Essentially, LMIs help determine if a system meets specific performance or stability requirements through linear matrix constraints.