Discrete-time Lyapunov stability of large matrices
Some techniques for analyzing the discrete-time stability of large matrices are proposed. These techniques combine Lyapunov theory and Krylov subspace methods. All the proposed methods need the computation of an approximate invariant subspace. Any good large eigensolver can be used for this step. The idea of the methods is to decompose the matrix into two blocks: a small block, obtained by Krylov-type methods, on which the classical discrete Lyapunov theory is applied and a large block whose either norm or its numerical radius is estimated. Using these two informations and some perturbation theory, one can justify mathematically the stability/instability of the matrix. Several numerical examples illustrate the behavior of the proposed method.
scientific article; zbMATH DE number 1423338
scientific article