Stability Analysis of the Interval Systems Based on Linear Matrix Inequalities

Positive definiteness and Hurwitz stability of the interval systems are discussed. A linear matrix inequality representation is introduced to simplify the analysis of the interval system. First, it is shown that the interval matrix can be stable if it has 2 conditions. Afterward, they converted to linear matrix inequalities for simplifying the conditions solution. A Lyapunov function is introduced to prove the new representation based on linear matrix inequalities.