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Low-rank iterative methods for periodic projected Lyapunov equations and their application in model reduction of periodic descriptor systems. (English) Zbl 1305.65158

Summary: We discuss the numerical solution of large-scale sparse projected periodic discrete-time Lyapunov equations in lifted form which arise in model reduction of periodic descriptor systems. We extend the alternating direction implicit method and the Smith method to such equations. Low-rank versions of these methods are also presented, which can be used to compute low-rank approximations to the solutions of projected periodic Lyapunov equations in lifted form with low-rank right-hand side. Moreover, we consider an application of the Lyapunov solvers to balanced truncation model reduction of periodic discrete-time descriptor systems. Numerical results are given to illustrate the efficiency and accuracy of the proposed methods.

MSC:

65K10 Numerical optimization and variational techniques
93C55 Discrete-time control/observation systems
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