New sufficient conditions for p-th moment stability of uncertain delay differential equation

Abstract

Uncertain delay differential system is an important mathematical model. Stability is a basic problem of uncertain delay differential system. Delay and uncertain interference often lead to changes in the stability of the system. Establishing the judgment of the stability of uncertain delay differential system conditions is very important. Based on the strong Lipschitz condition, the judgment of p-th moment stability for uncertain delay differential equations (UDDEs) has been investigated. Actually, the strong Lipschitz condition is assumed that it only relates to the current state, it is difficult to be employed to determine the stability in p-th moment for the UDDEs. In this paper, we consider two kinds of new Lipschitz conditions containing the current state and the past state, which are more weaker than the strong Lipschitz condition. Meanwhile, new sufficient theorems and corollaries under the new Lipschitz conditions as the tools to judge the p-th moment stability for the UDDEs are proved. Some examples explain the rationality of the corresponding theorems and corollaries.