Controller and control method for internal combustion engine

A controller for an internal combustion engine, wherein the internal combustion engine includes cylinders, a catalytic converter configured to purify exhaust gas and configured to store oxygen, and an exhaust sensor located at a downstream side of the catalytic converter and configured to detect oxygen, the controller comprising:

• processing circuitry, wherein:
• the processing circuitry is configured to execute a richening process that supplies the catalytic converter with exhaust gas having an air-fuel ratio that is rich until the exhaust sensor detects that the exhaust gas has a rich air-fuel ratio;
• after the exhaust sensor detects that the exhaust gas has a rich air-fuel ratio in the richening process, the processing circuitry is configured to execute an air supplying process that supplies the catalytic converter with air until the exhaust sensor detects that the exhaust gas has a lean air-fuel ratio;
• the processing circuitry is configured to execute a stored oxygen capacity estimating process that estimates a stored oxygen capacity of the catalytic converter by cumulating an amount of air supplied to the catalytic converter until the exhaust sensor detects that the exhaust gas has a lean air-fuel ratio in the air supplying process;
• and
• the air supplying process includes stopping fuel supplied to one or more of the cylinders and performing combustion at an air-fuel ratio that is less than or equal to a stoichiometric air-fuel ratio in remaining one or more of the cylinders so that the cylinders supply the catalytic converter with exhaust gas, which as a whole, is controlled to have a lean air-fuel ratio.