In the first sentence, you can leave out the is. In the second, because of the meaning of instructed you can't use was. You could say, As he was instructed by the boss in our previous meeting, he .... Now if you change the verb to discuss, you can say As was discussed in our previous meeting, he ... Here you can leave out the was. So I'm not sure there is a clear pattern.

hjs: Perhaps you have encountered the older English terminology which would read this way; "As is beknown to all...etc." Just use the modern form, which would be written as; "As is known to all...etc."

Sorry, I didn't fully answer your question. You can say "as everyone knows,..." The phrase "as is known" is OK but a bit more formal and I don't think sounds as good. For me, it's better to use the active voice.

I don't know how to explain the meaning in terms of omission of words. This is my explanation : "as instructed" means - "according to the instructions you already were given" "as described" means - "according to the description you already were given" e.g. "as described in the advertisement, the car was very fast" "as explained yesterday, you need to travel to the meeting" "as instructed by manager, I will give you a refund" Kind regards, Michael

I think the omission part of the second sentence is "he had been". As (he had been) instructed in our previous meeting, he has submitted a brief to the firm's architect. So they are not worth a comparison...