Stability analysis of uncertain simple pendulum equation ^*

Abstract

The law of motion of a simple pendulum system is described by an uncertain simple pendulum equation which is a second-order uncertain differential equation driven by Liu process. The stability of a simple pendulum system refers to whether the system tends to the equilibrium state under small perturbation. In order to discuss the sensitivity of the uncertain simple pendulum equation to the perturbation in the initial state, we give the concept of many kinds of stability of the uncertain simple pendulum equation, including almost deterministic stability, distributional stability and exponential stability. And, the sufficient conditions of almost deterministic stability, distributional stability and exponential stability of the uncertain simple pendulum equation are proved respectively.