Sounds like another school project...

You could limit your 'friendly' pets to weighing 20kg or less. Then cover your floor in Pressure mats that trigger over 35kg. Finally it would take two consequive triggers of the mat for an alarm condition (accounts for your 'friendly' pet jumping down from a high level).

Process your IR sensor (or even camera video) output by a DSP to determine the size of your target. Anything over a given size is considered 'not friendly'. Add-in further intelligent processing to descriminate between pet movement and habits and the kind taken by an intruder. It's unlikely your pet will open your fridge, drawers and cupboards... and an intruder is unlikely to spend time at the feeding bowl, grit-tray or curl-up in a warm corner for a couple of hours.

Folks have forgotten about permiter protection. If a house is secure, pets will enter/exit via a cat-flap for example. Intruders will enter via doors, windows and through the roof. Everyone want's to put up volumetric protection nowadays - because it's cheap, easy to deploy and it maximises the sellers/installers profits. Perimeter protection is more costly, but in a domestic environment is a far better option.

Finally, cover your house in standard PIR sensors, limit your pets to cold-blooded species (like Lawyers and Bank Managers).

Please make cheques payable to Melanie...