OUTPUT FEEDBACK STABILIZATION AND RELATED PROBLEMS - SOLUTION VIA DECISION METHODS.

Abstract

Given an unstable finite-dimensional linear system, the output feedback problem is, first, 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. The 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 their solution. The first part of the output feedback problem is solvable with a finite number of rational operations, and the second with a finite number of polynomial factorizations. Other areas of application of the algorithm are described: multivariable stability and positivity tests, inverse stability problems, low order observer and controller design, and nonlinear programming. An alternative computational procedure is proposed for tackling such problems directly. Show more