Methods and systems are provided for estimating an engine exhaust pressure based on outputs from an exhaust oxygen sensor. In one example, a method may include estimating an exhaust pressure of exhaust gas flowing through an engine exhaust passage based on a difference between a first output of an oxygen sensor disposed in the exhaust passage and a second output of the oxygen sensor and then adjusting engine operation based on the estimated exhaust pressure. As one example, both the first and second outputs may be taken while operating the sensor in a variable voltage mode, after increasing a reference voltage of the oxygen sensor from a lower, first voltage to a higher, second voltage.

A control device for an internal combustion engine includes first and second intake ports (16a, 16b) independent of each other, and first and second fuel injection valves (30a, 30b) provided for the first and second intake ports (16a, 16b), respectively, in each cylinder. Under a situation where an exhaust variable valve mechanism (38) is controlled such that a first exhaust valve (32a) is opened earlier than a second exhaust valve (32b), first and second air-fuel ratios A/F1, A/F2 are respectively obtained in a first half and a second half of an exhaust stroke. When the obtained first air-fuel ratio A/F1 (or the second air-fuel ratio A/F2) is lean, a fuel injection amount in a next cycle by the first or second fuel injection valve (30a, 30b) corresponding to the first air-fuel ratio A/F1 (or the second air-fuel ratio A/F2) that is lean is reduced.

An air-fuel ratio control device switches a target air-fuel ratio from a lean set air-fuel ratio to a rich set air-fuel ratio after judging that an air-fuel ratio of an outflowing exhaust gas has become a stoichiometric air-fuel ratio and an oxygen storage amount of an exhaust purification catalyst has become a switching reference storage amount, and makes an average value of the target air-fuel ratio the stoichiometric air-fuel ratio to less than the lean set air-fuel ratio, from after the estimated value of the oxygen storage amount has become the switching reference storage amount or more until judging that the air-fuel ratio of the outflowing exhaust gas has become the stoichiometric air-fuel ratio if the estimated value of the oxygen storage amount becomes the switching reference storage amount or more before judging that the air-fuel ratio of the outflowing exhaust gas has become the stoichiometric air-fuel ratio.

A three-way catalyst, an NSR catalyst, and an SCR catalyst are provided in this order for an exhaust gas passage, wherein the air-fuel ratio (AFR) is set to a first AFR which is a rich AFR before the AFR is switched from a theoretical AFR to a lean AFR, and then the AFR is set to a second AFR which is higher than the first AFR and lower than the theoretical AFR if a NOx occlusion amount is less than a threshold value during a period until an NH.sub.3 adsorption amount of the SCR catalyst becomes a predetermined adsorption amount, while the AFR is set to a third AFR which is higher than the first AFR and lower than the second AFR if the NOx occlusion amount is not less than the threshold value.