In this study, two issues regarding the Bloch chaotic system are investigated. Firstly, the invariant set and the solution bound for the Bloch chaotic system are derived. Subsequently, the derived solution bound can be applied to facilitate control design. The significant contribution of this paper is that since the solution bound of the Bloch chaotic system is derived, exponential synchronization can be achieved using a simple linear control which is very easy implemented. Finally, two numerical examples are provided to demonstrate the feasibility and correctness of the obtained results.