Sentence examples for ultimate bounds from inspiring English sources

When disturbances are periodic, frequency analysis technique obtains a less conservative estimate of the ultimate bound of the system, indicating that disturbances with high frequencies lead to relatively small ultimate bounds.

These notions allow us to develop less conservative ultimate bounds for neuroadaptive controllers as compared to ultimate bounds derived using classical boundedness and ultimate boundedness notions.

Meanwhile, the ultimate bounds of the generalized chaotic system about its all variables are induced by the ultimate bounds of the system about its partial variables.

end{aligned} (28) We will now proceed to employ the quantum estimation techniques necessary to find the ultimate bounds on the measurement errors we have explicitly found above.

In this section, we apply quantum estimation techniques to find the ultimate bounds on the precision of measurements of parameters of the Earth.

A novel parameter mapping is proposed to obtain a simple relationship between the design parameter and the ultimate bounds of error trajectories.

for positive definite, and are positive constants satisfying and,, and —guarantees that there exists a positively invariant set such that, where, and the solution,, of the closed-loop system given by (4.1), (4.2), (4.15), and (4.17) is ultimately bounded for all with ultimate bound,, where (4.19).

for positive definite, and are positive constants satisfying and,, —guarantees that there exists a positively invariant set such that and the solution,, of the closed-loop system given by (4.1), (4.2), (5.2), and (5.4) is ultimately bounded for all with ultimate bound,, where, (5.6 .,,,, and and are positive constants satisfying and.

where satisfies (4.18), and are positive constants satisfying and,, —guarantees that there exists a positively invariant set such that, where, and the solution,, of the closed-loop system given by (4.1), (4.2), (4.15), and (4.21) is ultimately bounded for all with ultimate bound,, where is given by (4.19) with replaced by in and,.

Conversely, if a discrete-time nonlinear dynamical system is (globally) ultimately bounded with respect to uniformly in with an ultimate bound, then it is (globally) bounded with respect to uniformly in.

From (3), we know that (T t)) has an ultimate bound (T_{0}), therefore, (L t)) and (T^(t)) are ultimately bounded with some (M_{1}).