On numerical solutions of the Sylvester-observer equation, and the multi-input eigenvalue assignment problem

This dissertation is devoted to the study of numerical solutions of two important linear algebra problems arising in control theory: the Sylvester-observer matrix equation and multi-input eigenvalue assignment problem. Two new algorithms are proposed: one for each problem.;The timing and accuracy of the proposed algorithm for the multi-input eigenvalue assignment problem are comparable to those of the existing algorithms for small problems; but for large problems, the new algorithm is much faster.;The basis of these algorithms is a novel generalization of the classical Arnoldi method for constructing an orthonormal basis of the Krylov subspace. This generalization, besides its roles in the solutions of the two above mentioned problems, may be of independent interest and may find applications elsewhere.;The results of the dissertation should be of interest and useful to applied and computational mathematics as well as control theorists and practising control engineers. They are expected to contribute to the development of numerically effective control design software.;The algorithm for the Sylvester-observer equation constructs an orthogonal solution to the equation. From numerical and design points of view, it is highly desirable to have such a solution. None of the existing algorithms, however, constructs such a solution.