Model reduction of periodic systems: a lifting approach

Farhood, Mazen; Beck, Carl; Dullerud, Geir E.

doi:10.1016/j.automatica.2005.01.008

Cited by 34 publications

(26 citation statements)

References 13 publications

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“…, 9. The computed reduced-order model has subsystems of orders (9,10,10,11,10,9,10,11,11,11). Note that stability is preserved in the reduced-order system.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Such solutions can be well approximated by lowrank matrices. That means that we can find a matrix Z with a small number of columns such that ZZ T is an approximation to the solution G cr of PCALE (10). This matrix Z is referred to as a low-rank Cholesky factor of the solution of (10).…”

Section: Low-rank Adi Methodsmentioning

confidence: 99%

“…Let G cr be the solution of the projected PCALE (10). After the i-th iteration, the error G cr i − G cr can be computed from (13) recursively as…”

Section: Adi Methods For Causal Lifted Lyapunov Equationsmentioning

confidence: 99%

“…Lifted representations of periodic discrete-time systems play an important role in extending many theoretical results and numerical algorithms for linear timeinvariant systems to the periodic setting [6,10,33]. We consider here the cyclic lifted representation which was introduced first for standard periodic systems in [18].…”

Section: Periodic Descriptor Systemsmentioning

confidence: 99%

“…Such systems have received a lot of attention in the last 30 years, e.g., in satellite attitude control, helicopter design, harmonic balance methods in nonlinear circuit design, and many more, see, e.g., [6,10,17,18,30,33]. Some control-theoretic concepts including controllability and observability, Gramians, Hankel singular values and balanced realization have been extended to periodic discrete-time descriptor systems with singular E k , see [8,9,24].…”

Section: Introductionmentioning

confidence: 99%

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Low-rank iterative methods for periodic projected Lyapunov equations and their application in model reduction of periodic descriptor systems

2014

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We discuss the numerical solution of large-scale sparse projected discrete-time periodic 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.

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“…, 9. The computed reduced-order model has subsystems of orders (9,10,10,11,10,9,10,11,11,11). Note that stability is preserved in the reduced-order system.…”

Section: Numerical Resultsmentioning

confidence: 99%

Section: Low-rank Adi Methodsmentioning

confidence: 99%

“…Let G cr be the solution of the projected PCALE (10). After the i-th iteration, the error G cr i − G cr can be computed from (13) recursively as…”

Section: Adi Methods For Causal Lifted Lyapunov Equationsmentioning

confidence: 99%