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A linear matrix inequality (LMI) approach to the design of robust adaptive neural modal observers is developed such that the state estimation error of the slow system is uniformly ultimately bounded (UUB) with an ultimate bound.
In the frame of time-delay system, we propose a parameter-dependent sufficient condition such that the closed-loop system with mixed event-triggering mechanism is globally uniformly ultimately bounded with a minimized ultimate bound for a certain disturbance attenuation level.
Therefore, all the solutions for (3) are uniformly bounded with an ultimate bound.
Thus all the solutions for system (4) are uniformly bounded with an ultimate bound.
Finally, stability of the overall system is proved that the relative position and relative attitude are uniformly ultimately bounded, and the size of the ultimate bound can be regulated small enough by control system parameters.
Then the nonlinear dynamical system (3.1), (3.2) is ultimately bounded with respect to uniformly in with ultimate bound where.
Similar(7)
That's the ultimate bind between the museum visitors and the artwork.
The investigation was conducted first by using classical thermogravimetric analysis (TGA) methods, which are based on ultimate chemically bound water estimation.
The observer estimation errors satisfying given stability conditions converge to an ultimate finite bound (within the specified boundary layer) with thickness O(T2) where T is the sampling period.
At each step of design, a feedback controller strengthened by nonlinear damping terms to counteract modelling errors is designed to guarantee input-to-state practical stability of the corresponding subsystem, and then parameter adaptions are introduced to reduce the ultimate error bound.
However, The ultimated lower bouppercan boundven.
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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