ðə sˈɪstəm ɪz kəntɹˈoʊləbəl æt tˈaɪm ɪf ænd ˈoʊnli ɪf ðɛɹ ɛɡzˈɪsts ɐ fˈaɪnaɪt sˈʌtʃ ðætðə mˈeɪtɹɪks, ˈɔːlsoʊ kˈɔːld ðə kəntɹˌoʊləbˈɪlᵻɾi ɡɹˈæmiən, ɡˈɪvən bˈaɪ
The system  is controllable at time  if and only if there exists a finite  such that the  matrix, also called the Controllability Gramian, given by