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Pole assignment for uncertain systems in specified regions by static output feedback

In this paper, the regional pole placement is studied. An analysis of robustness with respect to unstructured uncertainty, being 2-norm bounded, for linear systems is discussed. A bound on the maximum allowable perturbation is proposed. Moreover, a useful parameterization of such bound, based on the structure of the gain matrix and on a novel formula for computing the eigenvectors of any real matrix, is presented. Finally, the problem is formalized as an optimization one and solved by using a genetic-like algorithm. Two numerical examples show the effectiveness of the method.