Hurwitz Stability of Matrix Segment and The Common Solution Set of 2 and 3-Dimensional Lyapunov Equations

In this study, a necessary and sufficient condition is given for the stability of the convex combinations of n-dimensional two Hurwitz stable matrices. There is a close relationship between Hurwitz stability of the matrix segment and common solution to the Lyapunov equations corresponding to those matrices. Therefore, the results obtained in this area are important. In the case of existence, an algorithm that determines common solutions set is also given. A number of illustrative examples using this algorithm are given.