wˈʌn ʌvðə mˈeɪn ɹɪzˈʌlts ɪnðə θˈiəɹi ɪz ðætðə səlˈuːʃən ɪz pɹəvˈaɪdᵻd baɪ ðə lˈɪnɪɹ kwɑːdɹˈæɾɪk ɹˈɛɡjʊlˌeɪɾɚ ˌɛlkjˌuːˈɑːɹ, ɐ fˈiːdbæk kəntɹˈoʊlɚ hˌuːz ᵻkwˈeɪʒənz ɑːɹ ɡˈɪvən bᵻlˈoʊ.
One of the main results in the theory is that the solution is provided by the linear–quadratic regulator (LQR), a feedback controller whose equations are given below.