Engineering Analysis/Lyapunov Equation

From Wikibooks, open books for an open world
Jump to: navigation, search

[Lyapunov's Equation]

AM + MB = C

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:

M = -\int_0^\infty e^{Ax}Ce^{Bx}dx