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We discuss certain other, more general, decomposition methods, including the "smooth atomic decomposition," and the "generalized ϑ-transform".
By using the new augmented multiple Lyapunov function with more general decomposition approach, a novel sufficient condition for finite-time bounded with an H ∞ performance index is derived.
Firstly, a modified Lyapunov Krasovskii functional is constructed by employing the more general decomposition approach, the novel delay-dependent synchronization conditions are derived in terms of linear matrix inequalities, which can be easily solved by various convex optimization algorithms.
The main contribution of this paper is as follows: Firstly, we present a new augmented Lyapunov functional by employing the more general decomposition of a delay interval for a class of Markovian jump systems with mode-dependent time-varying delay.
By using the novel Lyapunov functionals with the more general decomposition of delay interval, a state feedback controller (3) can be designed such that the resulting closed-loop system is finite-time bounded with H ∞ performance.
Last but not the least, it is shown that less conservative and more general results can be derived since the time-varying delays are divided into a more general decomposition.
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Decomposition with IMFs is more general than decomposition with sinusoidal functions, in allowing time-varying amplitudes and frequencies for input signals.
Compared with three-component scattering model [2], in MCSM the helix and wire scattering mechanism corresponding to copolar and the cross-polar correlations are introduced for a more general target decomposition theorem.
Throughout this work, we use that dependency to decompose relations through a more flexible and general decomposition process, and by iterating this process, we find a mechanism to extract knowledge from the original relation.
We will use the more general form of the Karhunen Loève decomposition in (7).
The SVD represents a more general view of the eigenvalue decomposition for non-square matrices X.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com