Stability analysis for uncertain differential equation by Lyapunov’s second method

Abstract

Uncertain differential equation is a type of differential equation driven by Liu process that is the counterpart of Wiener process in the framework of uncertainty theory. The stability theory is of particular interest among the properties of the solutions to uncertain differential equations. In this paper, we introduce the Lyapunov’s second method to study stability in measure and asymptotic stability of uncertain differential equation. Different from the existing results, we present two sufficient conditions in sense of Lyapunov stability, where the strong Lipschitz condition of the drift is no longer indispensable. Finally, illustrative examples are examined to certify the effectiveness of our theoretical findings.