Summary: A function-objective model is proposed as a description of a controlled system. Based on this model, reconfigurable control problems of linear systems are analyzed, including whether the whole system can achieve reconfigurable control, which components should be selected, what control scheme should be adopted, whether the system can reach the desired control objectives, etc. Firstly, some concepts are defined such as function, objective, minimal reconfigurable unit condition, feasible set, etc. Then, based on these definitions, the function-objective model is established with the logical relation between functions and objectives and feasible sets of all objectives as its two main aspects. The reconfigurable control scheme can be determined by selecting a suitable feasible configuration in the top feasible sets, which are the feasible sets of top objectives. After the establishment of all the feasible sets offline, we can analyze the system reconfigurability offline or online. The method proposed can also be used to guide the design stage of controlled systems. Finally, a satellite model is given to illustrate the method.