New stability conditions for a class of linear time-varying systems

This paper considers the problem of asymptotic stability for linear time-varying systems of the form ẋ(t)=A(t)x(t). Some new stability conditions are proposed. First, two stability conditions for nonlinear time-varying systems are given by using non-monotonic Lyapunov functions. Then the results obtained are extended to the linear case, two stability conditions with infinite integral are derived. Furthermore, by using the top-floor function, a linear matrix inequalities (LMI) condition and an eigenvalue criterion for asymptotic stability of systems are presented. Comparing with the existing results, the conditions obtained allow both A(t)A(t) and Ȧ(t) are unbounded at t=+∞t=+∞. Some numerical examples are provided to show the effectiveness of the theoretical results.