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Abstruct-Civen an unstable finite-dimensional liar system, the output feedback problem is, f i to decide whether it is possible by memoryless linear feedback of the output to stabilize the system, and, second, to determine a stabilizing feedback law if such exists. This paper shows how this and a number of other linear system theory problems can be simply reformulated so as to allow application of known algorithms for solution of the existence qaestion, with the construction problem king solved by some extension of these known algorithms. The f i i part of the output feedback problem is solvable with a finite number of rational operations, and the second with a f i i e number of pdynomial factorizations. Other areas of application of the algorithm are d e s c r i i Stabiity and positivity tests, low-order observer and controller design, and problems related to output feedback. Alternative computational pracedures more or less divorced from the known algorithms are atso p r o p a l .

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The stability of two-dimensional, linear, discrete systems is examined using the 2-D matrix Lyapunov equation. While the existence of a positive definite solution pair to the 2-D Lyapunov equation is sufficient for stability, the paper proves that such existence is not necessary for stability, disproving a long-standing conjecture.