LMI (Linear Matrix Inequalities)

Linear Matrix Inequalities (LMIs) are mathematical expressions that involve matrices—arrays of numbers—where certain conditions must be met for these matrices to be considered valid. Specifically, LMIs require that certain matrix equations be positive semi-definite, meaning they do not have negative eigenvalues. This concept is widely used in control theory, optimization, and systems engineering, helping to solve complex problems related to stability and performance of systems by providing a way to express and enforce constraints mathematically, ensuring reliable and efficient solutions in various applications, including robotics, finance, and signal processing.