Uniform Asymptotic Stability by Indefinite Lyapunov Functions

Abstract

In this work, we consider Uniform Asymptotic Stability (UAS) of nonlinear time-varying systems. We utilize an indefinite signed polynomial of Lyapunov Function (LF) for the upper bound of the derivative of LF. This special bound is especially useful for perturbation problems. Compared to the ones in the literature we improve the upper bound of the LF and its related properties. Since UAS is the first step for input to state stability (ISS) and integral ISS, it should be thought that these improvements will give rise to new advances in real-world applications as well.