The above is my answer

 

Hi,

It looks like you are trying to work in two domains at the same time. That's allowed in some advanced specialized filter theory, but here i think you want to work in either the 's' domain or the 'z' domain, but not both. In other words, your final solution should be in terms of either 's' or 'z' but should not contain both in the same equation. That means either you have to transform a 'z' part into an 's' part or transform an 's' part into a 'z' part. Once you do that, you have everything in only one domain and so then you can use one of the methods for determining stability either in the 's' domain or in the 'z' domain which you probably already know how to do.