The invisible barrier refers to a somewhat unwritten rule followed by Japanese automakers. It isn't that the government stated specifically not to exceed some figure; however, it seems to be adhered to when it comes to cars being sold in Japan. Exported cars seem to be exempt from the rule.
With the Japanese economy expanding at the rate that it was in the 80s, so did the competition between Japanese automakers heat up. Nissan 300ZX's turbo version came out at 280 horsepower in 1989 and since then it has been the defacto figure makers aimed for but didn't want to exceed. Naturally, cars that originally offered power in lower ranges, slowly yet surely, also got bumped up to as far as it could within displacement limitations.
A pattern I have noticed was that 'top-end' versions of various cars approached roughly 100 horsepower per liter. So a 3-liter car like the 300ZX(Z32) should manage 300ps. It should be kept in mind that horsepower is only a figure and what really counts is the lower-end torque. Unlike the US, Japan uses the metric system so torque is measured in kilogram - meters. Interestingly, under optimal conditions, a liter approaches 10 kg-m. In the case of the above-mentioned Z32, the torque figure was 39.6 kg-m(27.8 kg-m for non-turbo).
Over 10 years have passed since then and it is not hard to even find top-end front-drives with specs matching the above trend. Many European auto manufacturers tend not focus on max horsepower while designing for a more stable torque band. It should also be noted that this barrier was only in terms of what was published and 'stated' in catalogs. It's probably not an overstatement to say that plenty of cars actually were designed to put out more, in stock condition. Tinkering with the engine would therefore far exceed those catalog figures.
An interesting site that converts all these units is here. You may have all your conversion calculations done there.