Development and stability analysis of algorithms for robust pole assignment of linear multi-input system

The first contribution of this dissertation is the development of a hybrid algorithm for solving the robust pole assignment problem. This algorithm calculates a matrix of right eigenvectors of near minimal condition number for the closed-loop system matrix in the manner of Kautsky, Nichols and Van Dooren (Int. J. Control, 41, pp. 1129-1155) and recovers the feedback gain matrix using Givens rotations and deflation in the manner of Petkov, Christov and Konstantinov (IEEE Trans. Auto. Control, AC-31, pp. 1044-1047). The algorithm uses only real arithmetic and is proven to solve the robust pole assignment problem. Numerical results from a Matlab implementation are included.;The second contribution is a weak stability analysis of an algorithm which uses back substitution to solve an upper triangular system of linear equations with multiple right-hand sides. The multi-input pole assignment problem is related to the multiple right-hand side problem because the solution is a matrix rather than a vector. An understanding of the stability analysis of an algorithm which solves the multiple right-hand side problem is essential before the more complicated multi-input pole assignment algorithms can be analyzed. Therefore, weak stability analysis should be used to analyze these algorithms.;The third contribution is a theoretical perturbation analysis and a weak stability analysis of a real-arithmetic version of the Kautsky, Nichols and Van Dooren algorithm. The error bound on the computed solution to the robust pole assignment problem is compared to a "best case" theoretical perturbation result and it is demonstrated that the algorithm of Kautsky, et al. has favorable numerical qualities.;The final contribution is a preliminary weak stability analysis of the hybrid algorithm. This analysis is based on several intermediate results on the condition number of a submatrix and are interesting by themselves. It is hoped that these results may be used in a more conclusive error analysis of this algorithm.