Model Reduction for Discrete-Time Switched Linear Time-Delay Systems via the H∞ Robust Stability

Birouche, Abderazik; Mourllion, Benjamin; Basset, Michel

doi:10.2316/journal.201.2011.1.201-2245

Cited by 12 publications

(8 citation statements)

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“…Considerable attention has been dedicated in recent years to the problem of MOR for linear switched systems. A class of methods that involves matching of generalized Markov parameters (known also as time domain Krylov methods) has been discussed in [4,3]; H ∞ type of reduction methods were developed in [43,11,44]. We mention some publications that are focused on the reduction of discrete LSS, such as [41] and [12].…”

Section: Introductionmentioning

confidence: 99%

Balanced truncation for linear switched systems

et al. 2018

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We propose a model order reduction approach for balanced truncation of linear switched systems. Such systems switch among a finite number of linear subsystems or modes.We compute pairs of controllability and observability Gramians corresponding to each active discrete mode by solving systems of coupled Lyapunov equations. Depending on the type, each such Gramian corresponds to the energy associated to all possible switching scenarios that start or, respectively end, in a particular operational mode.In order to guarantee that hard to control and hard to observe states are simultaneously eliminated, we construct a transformed system, whose Gramians are equal and diagonal. Then, by truncation, directly construct reduced order models. One can show that these models preserve some properties of the original model, such as stability and that it is possible to obtain error bounds relating the observed output, the control input and the entries of the diagonal Gramians. † Data-Driven System Reduction and Identification Group,

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Section: Introductionmentioning

confidence: 99%

Balanced truncation for linear switched systems

et al. 2018

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“…Notice that computational neuroscience often involves models of ever increasing computational complexity [35], our team has already invested significant efforts in reduction of model complexity. Another orientation work may be considered, in parallel to the studied stability constraints here, in investigating a reduction of model order [36,37], while guaranteeing its stability and maintaining desired nonlinear dynamic response.…”

Section: Discussionmentioning

confidence: 99%

Stability Constraints of Markov State Kinetic Models Based on Routh- Hurwitz Criterion

Sarmis

Orjuela²,

Bouteiller³

et al. 2015

J Comput Sci Syst Biol

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“…The disadvantage of these methods is that often there are no error bounds or the reduced order model need not be well-posed. Examples of such papers include [8], [9], [10], [11], [12], [13]. Note that to the best of our knowledge, the only algorithm which always yields a well-posed linear switched system of the same type as the original one and for which there exists an analytic error bound is the one of [13].…”

Section: Methods Based On Local Gramiansmentioning

confidence: 99%

Model reduction of linear hybrid systems

Gosea¹,

Petreczky²,

Leth³

et al. 2020

Preprint

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The paper proposes a model reduction algorithm for linear hybrid systems, i.e., hybrid systems with externally induced discrete events, with linear continuous subsystems, and linear reset maps. The model reduction algorithm is based on balanced truncation. Moreover, the paper also proves an analytical error bound for the difference between the input-output behaviors of the original and the reduced order model. This error bound is formulated in terms of singular values of the Gramians used for model reduction.

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Model Reduction for Discrete-Time Switched Linear Time-Delay Systems via the H∞ Robust Stability

Cited by 12 publications

References 0 publications

Balanced truncation for linear switched systems

Balanced truncation for linear switched systems

Stability Constraints of Markov State Kinetic Models Based on Routh- Hurwitz Criterion

Model reduction of linear hybrid systems

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