On asymptotic stability of linear time-varying systems

This paper is concerned with asymptotic stability analysis of linear time-varying (LTV) systems. With the help of the notion of stable functions, some differential Lyapunov inequalities (DLIs) based necessary and sufficient conditions are derived for testing asymptotic stability, exponential stability and uniformly exponential stability of general LTV systems. With the help of the concept of (non-uniformly) exponential stability, a class of upper-triangular LTV systems is carefully investigated based on the developed stability analysis approaches. A couple of numerical examples with some of them borrowed from the literature is provided to illustrate the effectiveness of the proposed theoretical results.