Balanced Reduction of Linear Periodic Systems

Longhi, Sauro; Orlando, Giuseppe

doi:10.1142/9789814447317_0139

Cited by 16 publications

(10 citation statements)

References 25 publications

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“…There, an operator-theoretic framework was used to give bounds similar to those that apply to time-invariant models. For discrete time-periodic linear systems bounds have been proven in [15], [16]. There, a special form of lifting isomorphism was used.…”

Section: B Previous Workmentioning

confidence: 99%

“…is often called a reachability Gramian. Assume there is a positive-definite block-diagonal solution to (14) (15) with and scalar. Notice that (14) is equivalent to (16) Now, assume we apply the same input signal to and .…”

Section: Reachability Lyapunov Inequalitymentioning

confidence: 99%

“…Still we would like to let for many periodic systems. In [13], [15], and [16], a bound for balanced discrete time-periodic systems is presented. We can also derive this bound:…”

Section: Periodic Systemsmentioning

confidence: 99%

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Balanced Truncation of Linear Time-Varying Systems

Sandberg

Rantzer

2004

IEEE Trans. Automat. Contr.

140

107

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In this paper, balanced truncation of linear time-varying systems is studied in discrete and continuous time. Based on relatively basic calculations with time-varying Lyapunov equations/inequalities we are able to derive both upper and lower error bounds for the truncated models. These results generalize well-known time-invariant formulas. The case of time-varying state dimension is considered. Input-output stability of all truncated balanced realizations is also proven. The method is finally successfully applied to a high-order model.

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Section: B Previous Workmentioning

confidence: 99%

Section: Reachability Lyapunov Inequalitymentioning

confidence: 99%

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Balanced Truncation of Linear Time-Varying Systems

Sandberg

Rantzer

2004

IEEE Trans. Automat. Contr.

140

107

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“…Such equations appear in solving periodic state-feedback problems and computing gradients for optimal periodic output feedback problems [21,24]. Further applications related to discrete-time periodic systems include the solution of Riccati equations [4], minimal realisations [22] and model reduction [15,23].…”

Section: Introductionmentioning

confidence: 99%

Large periodic Lyapunov equations: Algorithms and applications

Kreßner

2003

2003 European Control Conference (ECC)

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Two algorithms for the solution of discrete-time periodic Lyapunov equations are presented. The first one is a variant of the squared Smith iteration, which is solely based on matrix multiplications and thus attractive to parallel computing environments. The second algorithm is based on Krylov subspaces and employs a recently developed variant of the block Arnoldi algorithm. It is particularly suited for periodic Lyapunov equations with large and sparse coefficient matrices. We also demonstrate how these methods can be applied to balanced truncation model reduction of periodic discrete-time systems and the solution of periodic Riccati equations.

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“…In (Lall et al, 1998) an operator theoretic framework for balanced truncation of time-varying system is presented together with an error bound. Error bounds on truncated periodic balanced time-variable systems in discrete time can be found in (Longhi and Orlando, 1999;Varga, 2000).…”

Section: Introductionmentioning

confidence: 99%

Balanced Model Reduction of Linear Time-Varying Systems

Rantzer

2002

IFAC Proceedings Volumes

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Balanced Reduction of Linear Periodic Systems

Cited by 16 publications

References 25 publications

Balanced Truncation of Linear Time-Varying Systems

Balanced Truncation of Linear Time-Varying Systems

Large periodic Lyapunov equations: Algorithms and applications

Balanced Model Reduction of Linear Time-Varying Systems

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