Dalam tesis ini dibahas sistem linear atas aljabar Ore. Suatu Aljabar Ore adalah suatu aljabar dari polinomial non-komutatif dimana dalam operator fungsional memenuhi aturan komutatif tertentu. Di dalam kerangka matematika ini, beberapa kelas yang berbeda dari sistem kontrol linear dapat dipelajari secara bersamasama, seperti, sistem diferensial biasa time-varying, sistem diferensial time-delay, persamaan diferensial parsial, multidimensional sistem diskret, dan lain-lain. Dengan menggunakan homologi aljabar ,diberikan suatu algoritma efektif untuk memeriksa keterkendalian dan keterparametrisasian sistem linear atas aljabar Ore.

In this thesis studied linear system over Ore algebras. An Ore algebra is an algebra of non-commutative polynomials in functional operators which satisfy certain commutation rules.Within this mathematical framework, some different class of linear control systems can study simultaneously, such as time-varying ordinary differential system, differential time-delay system, partial differential equation, multidimensional discrete system, etc. Using homological algebra, given an efective algorithm to check controllability and parametrizability of linear system over Ore algebra

Kata Kunci : Integral Nonlinear Henstock, Ruang Banach, Ore algebra, linear system over Ore algebras, controllability, parametrizability, parametrization, Grobner basis.