An algorithm for the stabilization of large single-input time-invariant linear control systems by partial eigenvalue assignment is presented. The authors consider also a modified partial eigenvalue assignment problem in which one may choose not only the feedback matrix but also the system input matrix and propose an algorithm for its solution. Both algorithms are based on the implicitly restarted Arnoldi method, which is used repeatedly until no more eigenvalues with nonnegative real parts are found. The algorithms do not require the state matrix to be stored or factored and are well suited for control systems that require the reassignment of a few eigenvalues. Numerical experiments involving systems of order 2000 are described.
For the entire collection see [Zbl 0972.00034].