Title : Structure preserving iterative methods for periodic projected Lyapunov equations and their application in model reduction of periodic descriptor systems

Authors : Peter Benner, Mohammad-Sahadet Hossain

Abstract : In this paper, we develop structure preserving iterative schemes to solve the periodic discrete-time projected Lyapunov equations associated to analysis and design of discrete-time descriptor systems exploiting the reflexive generalized inverses of the periodic matrices associated with these systems. In particular, we extend the Smith method to solve the large-scale projected periodic discrete-time algebraic Lyapunov equations in lifted form. A low-rank version of this method is also presented, avoiding the explicit lifted formulation and working directly with the periodic matrix coefficients. Moreover, we consider an application of the Lyapunov solvers in balanced truncation model reduction of periodic discrete-time descriptor systems. Numerical results are given to illustrate the efficiency and accuracy of the proposed methods.

Journal : Numerical Algorithms, Springer Volume : 76 Year : 2017 Issue : 4
Pages : 881–904 City : Edition : Editors :
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