On stability of linear time-varying systems

This paper presents two easy-to-check criteria that test respectively the necessary condition for the asymptotic stability and the sufficient condition for the instability of linear time-varying systems. A necessary and sufficient condition, defined in terms of the newly introduced concept of the mode-vectors is also given for stability of linear time-varying systems. An algorithm for finding the mode-vectors is presented. Several examples are given to illustrate the applications of the results in the paper.