To estimate an amount of reducing agent adsorbed to a selective reduction type NOx catalyst with a higher degree of precision while maintaining a condition in which NOx can be purified by the selective reduction type NOx catalyst, the present invention includes: an upper limit value calculation unit that calculates an upper limit value of a reducing agent amount that is adsorbed to the selective reduction type NOx catalyst when the reducing agent is supplied continuously during a steady state operation in an internal combust ion engine; and an estimation unit that estimates an upper limit value calculated by the upper limit value calculation unit when the reducing agent is supplied for at least a predetermined time during the steady state operation in the internal combustion engine to be the reducing agent amount adsorbed to the selective reduction type NOx catalyst at that time.