Dynamical systems (DS) has been applied to robot contact tasks, such as grinding and force tracking, because of its motion replanning capability after disturbances. However, when faced with robot tasks like peg-in-hole assembly that can be decomposed into multiple subtasks, DS can still replan at motion level but lacks the ability to plan subtasks after disturbances from humans. In this paper, we propose a DS-based peg-in-hole assembly method using a linear temporal logic (LTL) planner with impedance control to make up for the lack of task-level replanning. In our approach, the motion policy (even force profile) of each assembly subtask is represented as a single DS, and the switching of subtasks is determined by the LTL planner. Due to the motion replanning of DS and the task planning capacity of the LTL planner, the human collaborator is allowed to interact directly with the robot. After interactions, the robot will replan itself and continue to perform its task smoothly according to our assembly strategy. The proposed method is carried out in experiments on a six-degrees-of-freedom collaborative robot. The experimental results demonstrate the effectiveness of this method.