A manipulation variable generating unit 7 for generating a target air-fuel ratio KCMD to converge the output of an oxygen concentration sensor 5 disposed downstream of a catalytic converter 3 in an exhaust system E as a plant to a given target value has a plurality of estimators for generating data indicating estimated values of the output of the oxygen concentration sensor after a dead time of the exhaust system E or a total dead time which is the sum of the dead time of the exhaust system E and a dead time of a system comprising an engine control unit 8 and an internal combustion engine 1, according to respective different algorithms. The manipulation variable generating unit 7 generates the target air-fuel ratio KCMD according to an adaptive sliding mode control process using a value selected from the estimated values or a combined value representing a combination of the estimated values.