Sentence examples for are proven using from inspiring English sources

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).

Linear and non-linear stability results, including A-stability, L-stability and B-stability are proven using the energy method for general initial value problems.

The TDC algorithm design is created with a low-order dynamic model, and its superior performances are proven using a real-time control experiment.

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

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

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