Sentence examples for existing bounded from inspiring English sources

Using this condition and the existing bounded real lemma, we develop systematic design methods for H2 and mixed H2/H∞ control of 2-D systems, and an application of the controller design methods to the control problem of a metal rolling process is demonstrated in this paper.

The example shows that the bound in Theorem 3.2 is better than the existing bounds in Theorem 4 in [11] and Theorem 4 in [10] in some cases.

The example shows that the bound in Theorem 3.3 is better than the existing bounds in Theorem 4 in [11], Theorem 4 in [10] and Theorems 2.1, 2.2 in [9].

The example shows that the bounds in Theorem 2.1 and Theorem 2.2 are better than the existing bounds.

The example shows that the bounds in Theorem 4.1 are better than the existing bounds in Theorem 1 in [2] and Theorem 1 in [3].

Some related issues were already considered in the literature for the 2-dimensional case S2; our results are new or improve the existing bounds even in these special circumstances.

Additionally, the derivatives of (B_{N}(x;f)) also satisfy the existing bounds of the corresponding derivatives of f (see [26]) and possess the same convergence properties (see [16]).

Then, a new definition for uncertainty bounds is presented in order to eliminate the type-reduction process in IT2 FLSs and to increase accuracy of the existing uncertainty bounds in the literature.

This illustration compares the proposed lower bound with the existing lower bounds from [3] and [4], showing that the proposed lower bound is tighter.

Our new lower bound is sharper and more valid than other existing lower bounds in literature, which is a useful complement to the lower bound theory of discrepancies.

Sadler explained that Tessian is looking to apply its tech to in-bound email, in addition to its existing out-bound products.