This is the 13031st most frequent Russian word.
мадридским
"Мадридским" means "Madrid" as an adjective, relating to Madrid.
Here, 'мадридским' is used as an adjective derived from the city 'Madrid', describing the word 'art' (искусством) in terms of its origin or association with Madrid.
Я наслаждался мадридским искусством в музее.
I enjoyed the Madrid art in the museum.
In this sentence, 'мадридском' is used in a prepositional case form, agreeing with the noun 'фестивале' and indicating the specific festival associated with Madrid.
Она всегда мечтала об участии в мадридском фестивале.
She always dreamed of participating in the Madrid festival.
Here, 'мадридский' is in its basic nominative masculine singular form, qualifying the noun 'ресторан' and indicating its Madrid origin.