Permanent cover or removable?

Last summer we built one of the Costco gazebos over our patio. We love it.

I'd also talk to your local permit office to find out the restrictions on building a permanent structure to cover the patio. Most cities have restrictions on the amount of covered area vs. total lot size (Floor Area Ratio), how close a permanent structure can be to the lot line, and other construction rules. Its no fun to get through the 1st day of construction and have the code enforcement come by to shut down your project.

Bruce

As already mentioned you will need to consider zoning setbacks as well as structural considerations - wind and snow loads and whether that existing slab can handle it. Having said all that there a ton of fun ways to get elemental coverage for an outdoor space like that - low sloped "slab" style roof, fabric structure, heck even a large floating glass roof to keep out rain and let in light and views!