Having been favourites to go straight back down when they were promoted in 2008, Stoke havedefied their critics to establish themselves in the Premier League, and they are often cited by fans and managers as an example to try to follow.
Last season they finished 13th, their lowest final position during their three Premier League campaigns, and secured a place in Europe by reaching the final of the FA Cup.
The Potters put themselves in a great position to reach the group stages of the Europa League with a 1-0 win over FC Thun on Thursday night, and they have travelled straight from Switzerland to Norwich ahead of Sunday's league clash.
Paul Lambert's Canaries began their campaign in promising fashion with a 1-1 draw at Wigan, and although QPR and Swansea were both beaten 4-0, Pulis believes all three sides have what it takes to do well.
He said: "We have had our way of doing things and we've stuck very rigidly to building up over three years and they will learn as they go along.
"I think the three clubs have got very good managers. You look at Paul Lambert, (Neil) Warnock and Brendan (Rodgers) and they have all done fantastic jobs in getting their teams promoted.
"It is a different challenge and a different set of rules. It is not a level playing field. You learn very quickly and you have to take things on board."
Pulis knows facing a promoted club in their first home match in the Premier League will present significant challenges for Stoke, and a trip back from Europe two days before is not ideal preparation.
Next weekend the Potters must also travel away to West Brom after the second leg of their clash with Thun, although at least that is at the Britannia Stadium.
Pulis said: "It is going to be a difficult game because of the match (on Thursday) and then we come back and we play two away games, which is a tough call for the club. We will face the challenge head on and do our best.
"I would have preferred to have played Norwich further down the line because it is their first home game in the Premier League.
"If you go back to when we came up, we faced Aston Villa in our first game at home and we ended up winning 3-2.
"Norwich is a fantastic club; they have a chairman who is a massive supporter, it is old-fashioned in the respect of tradition and they have a great group of supporters.
"Norwich have sold out, they are a very well-supported club and the atmosphere will be fantastic. We have to roll our sleeves up and make sure we have a clear mind and give it the best we possibly can.
"As soon as the fixtures came out I saw we had three home games against Chelsea, Liverpool and Manchester United and then to get the games away from home we did was tough. I would have much preferred it the other way around."