# Engineering Analysis/Lyapunov Equation

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[Lyapunov's Equation]

Where *A*, *B* and *C* are constant square matrices, and M is the solution that we are trying to find. If *A*, *B*, and *C* are of the same order, and if *A* and *B* have no eigenvalues in common, then the solution can be given in terms of matrix exponentials: