A design algorithm of static output feedback control for eigenstructure assignment

Abstract

Eigenvectors determine the sensitivity and robustness properties of the corresponding eigenvalues. Hence, their assignment is as important as eigenvalue assignment. The algorithm of this paper assigns eigenvectors in a most explicit and therefore the best form - assigning a linear combination of the basis vectors of each eigenvector. Compared to the most recent and similar algorithms, which assign the eigenstructure in two consecutive groups, this algorithm has three additional advantages: (1) the explicit and analytical solution of a key matrix equation pair is derived; (2) a very complicated similarity transformation and numerical operation for assigning the second group of eigenvalues/vectors is eliminated; and (3) the duality of the whole problem is fully revealed in the actual design solution and computation - this makes the algorithm valid to the formally prohibitive situation in which all eigenvalues are complex-conjugate but the number of system outputs is odd.