Numerical Algorithms for Eigenvalue Assignme by Constant and Dynamic Output Feedback

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In this paper, we propose algorithms for eigenvalue assignment (EVA) by constant as well as dynamic output feedback. The main algorithm is developed for single-input, multioutput systems and the results are then extended to multiinput, multioutput systems. In computing the feedback, use is made of the fact that the closed-loop eigenvalues can “almost always” be assigned arbitrarily close to desired locations in the complex plane, provided the system satisfies the condition m + p < n, where m,p, and n are, respectively, the number of inputs, outputs, and states of the system. The EVA problem has been treated as a converse of the algebraic eigenvalue problem. The proposed algorithms are based on the implicitly shifted QR algorithm for solving the algebraic eigenvalue problem. The performance of the algorithms is illustrated by means of several numerical examples. © 1989 IEEE



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