Stability is one of the most important problems in the analysis and synthesis of dynamical systems. Almost every workable system is designed to be stable. If a system isn’t stable, it is usually of no use in practice. It is well known that a linear time-invariant system is stable if and only if all eigenvalues of the system matrix A have negative real parts. However, this is no longer true for linear time-varying systems. Recently I made a presentation about stability of LTV systems in IUT. In this presentation some obtained results were discussed. PPT files of this seminar can be downloaded by hyperlink below.