Linear Matrix Inequalities

Linear Matrix Inequalities (LMIs) are mathematical expressions that involve matrices, which are rectangular arrays of numbers. An LMI typically takes the form of a matrix inequality, such as \( A + B \) > 0, where \( A \) and \( B \) are matrices, and the inequality indicates that the resulting matrix is positive definite (all its eigenvalues are positive). LMIs are used in various fields, including control theory, optimization, and signal processing, to represent constraints or conditions that must be satisfied, allowing for the analysis and design of systems in a structured and efficient way.