Control device for prompting battery diagnosis and vehicle having such control device

A control device for controlling a vehicle in which a power storage device and an auxiliary battery are installed, and also from which auxiliary battery, electric power is supplied, the control device comprising:

• a processor that estimates a full charge capacity of the power storage device;
• first memory that stores the full charge capacity estimated by the processor;
• and
• a transmitter configured to communicate with an information terminal, wherein:
• the auxiliary battery is configured to be electrically disconnectable from the vehicle;
• and
• the transmitter transmits, to the information terminal, a notification prompting diagnosis of the power storage device, in response to an elapsed time from a first point in time at which the vehicle was started up a prior time to a second point in time at which the vehicle was started up this time being greater than a predetermined value.