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Bondarko, V. A.; Fradkov, Alexander L.

doi:10.1023/a:1023230128592

Cited by 8 publications

(3 citation statements)

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“…13 5. To overcome the latter difficulty the third method of studying w Chowdecompositions (that is more "explicit" than the second one) was developed in [BoL16,§3] 6. Recall that the behaviour of the categories D c (−) and of the "weights" of their objects is quite similar to that of mixed Q l -complexes of étale sheaves and their weights as studied in [BBD82].…”

Section: On Relative Motives and Chow Weight Structures For Them: A Rmentioning

confidence: 99%

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On constructing weight structures and extending them to idempotent completions

Bondarko

Sosnilo

2018

Homology, Homotopy and Applications

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In this paper we describe a new method for constructing a weight structure w on a triangulated category C.For a given C and w it allows us to give a fairly comprehensive (and new) description of triangulated categories containing C as a dense subcategory (i.e., of subcategories of the idempotent completion of C that contain C; we call them idempotent extensions of C) to which w extends. In particular, any bounded above or below w extends to any idempotent extension of C; however, we illustrate by an example that w does not extend to the idempotent completion of C in general.We also describe an application of our results to certain triangulated categories of (relative) motives.

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Section: On Relative Motives and Chow Weight Structures For Them: A Rmentioning

confidence: 99%

“…It certainly follows that w Chow (B) also restricts to the union ∪ j∈Z D c δ≤j (B) that will be denoted by D c ef f (B). The latter fact is certainly (formally) weaker than the existence of all the restrictions to D c δ≤j (B); yet the authors do not know any proof of it that does not rely on [BoL16].…”

mentioning

confidence: 96%

On constructing weight structures and extending them to idempotent completions

Bondarko

Sosnilo

2018

Homology, Homotopy and Applications

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“…[8], [9], [10]). While this was a reasonable approach at a time when analysis of linear delayed and PDE systems [11] was considered computationally challenging, recent work has shown that model-based computational evaluation of the input-output properties of linear delayed and PDE systems can be performed efficiently and accurately [12], [13]. As a result, the framework for IQC-based analysis has shifted, where now delayed and PDE components are contained in the nominal subsystem and nonlinearities and uncertainties are isolated in the unmodelled subsystem.…”

Section: Introductionmentioning

confidence: 99%

Integral Quadratic Constraints with Infinite-Dimensional Channels

Talitckii

Peet

Seiler

2023

2023 American Control Conference (ACC)

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Modern control theory provides us with a spectrum of methods for studying the interconnection of dynamic systems using input-output properties of the interconnected subsystems. Perhaps the most advanced framework for such inputoutput analysis is the use of Integral Quadratic Constraints (IQCs), which considers the interconnection of a nominal linear system with an unmodelled nonlinear or uncertain subsystem with known input-output properties. Although these methods are widely used for Ordinary Differential Equations (ODEs), there have been fewer attempts to extend IQCs to infinitedimensional systems. In this paper, we present an IQC-based framework for Partial Differential Equations (PDEs) and Delay Differential Equations (DDEs). First, we introduce infinitedimensional signal spaces, operators, and feedback interconnections. Next, in the main result, we propose a formulation of hard IQC-based input-output stability conditions, allowing for infinite-dimensional multipliers. We then show how to test hard IQC conditions with infinite-dimensional multipliers on a nominal linear PDE or DDE system via the Partial Integral Equation (PIE) state-space representation using a sufficient version of the Kalman-Yakubovich-Popov lemma (KYP). The results are then illustrated using four example problems with uncertainty and nonlinearity.

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