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As with most disruptive movements, the fallout is mostly in the gap between the original system and the new one.
This yields a direct connection between the original system ( S λ ) and the augmented system ( S λ ).
According to the relation between the original system and the converted one, the state of the original system is proved to be bounded.
For RDOEL whose auxiliary dynamics is a chain of integrators (RDOELI), we provide a complete constructive algorithm which presents not only a coordinate transformation between the original system and a nonlinear observer canonical form, but also the minimum number of integrators needed to perform RDOELI.
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The Tail Probability Equivalent Linear System (TPELS) is the ELS where the difference in terms of tail probability between the TPELS and the original system is minimized.
From Figures 9 and 10, we see a significant quantitative discrepancy between the numerical solution of the original system and the approximated solution.
Given a set of predetermined expansion points, an exact expression for the error between the output moment of the original system and that of the reduced-order system, related to each expansion point, is derived first.
We present an a posteriori computable upper bound for the H2-norm of the error system defined as the system whose transfer function corresponds to the difference between the transfer function of the original system and the transfer function of the reduced system.
As shown in Figure 7, the only difference between this virtual system and the original system is that the collision region of the packet at any time t1 is shifted from [t1 - τ,t1 + τ] to [ ⌊ t 1 2 τ ⌋ 2 τ, ⌊ t 1 2 τ + 1 ⌋ 2 τ ].
It suffices to establish the correspondence between the Lagrangian equivalent system and the original system.
Also, several conditions about the invariance of the stabilizability or controllability between the state-space realizations of the original system and the compensated system are shown.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com