Sentence examples for are proved using from inspiring English sources

The latter properties are proved using general averaging and Lyapunov stability.

The stability and robustness of the two proposed schemes are proved using Lyapunov stability theory.

The unconditional stability and the high-order convergence are proved using the Fourier analysis method.

The estimates are global in time and are proved using a variation of Morawetz multipliers.

Almost all such results are proved using the PCP Theorem (and its several variants), one of the deepest theorems in computational complexity.

The stability and convergence of the proposed scheme are proved using Schwarz׳s inequality condition and Frobenius norms.

Finite time stability and convergence are proven using Lyapunov theory.

The boundedness and convergence properties of the closed-loop signals are proven using Lyapunov׳s stability theory.

The stability and convergence of the scheme are proven using the discrete energy method.

The stability and robustness properties of the controller are proven using a smooth and homogeneous strict Lyapunov function (LF).

The validity and effectiveness of the proposed method are proven using simulation and laboratory tests.