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Comparison of four numerical algorithms for solving the Liapunov matrix equation

This paper summarizes four alternative methods for computing the solution to the Liapunov matrix equation. A comparison of the methods is presented, along with sample computer runs. The necessity for solving this equation arises not only in certain phases of nonlinear stability analysis, but also in the design of optimal systems with fixed control structures. A more general form of this equation, which often appears in structural analysis, can be handled directly by one of the methods, and by the others with minor modifications.