In this paper, a condition of the global controllability for a linear and nonlinear systems is obtained. The methods are based on the exponential of even diagonalizable or non-diagonalizable matrix. Matrix computation is one of the most important, and useful, concepts in science and even our world. In this way non-diagonalizable matrices are a large class of this eld. To the best of our knowledge, no study have yet been attempted for this computation. Just the Jordan canonical form method exists in this way. In fact we give interesting recurrence relation for the characteristic polynomial of non-diagonalizable matrix, then by solving this recurrence relation we obtain the power of this matrix. Finally, we can use this approach for checking the controllability of systems with these matrices. Illustrative example is included to demonstrate the validity and applicability of the technique.

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