Sentence examples for is proved using a from inspiring English sources

Stability is proved using a Lyapunov approach.

The stability analysis in the paper is proved using a well-known Lyapunov stability theory.

The existence of a variational solution is proved, using a special property of the nonlinear operator.

The applicability of the method is proved using a real-time structure with an RST control algorithm.

The exponential stability of the observer is proved using a set of Lyapunov functionals and its performances are illustrated by simulation.

The complex eigenproblem for materials whose mechanical properties are dependent on frequency is solved by a fast iterative approach, whose validity is proved using a four-parameter fractional derivative model.

We remark that a stronger result is proved in [4] than that used above, namely that the optimal mappings are strictly convex and Hölder continuous whereas in [24] only strict convexity and continuity is proved, (using an earlier version of [4] which assumes condition A3w without the orthogonality restriction on (xi ) and (eta )).

Convergence is proven, using a Lyapounov function.

The stability of the closed-loop system is proven using a Lyapunov approach.

Although the overall system is infinite dimensional, convergence of the observer is proven using a standard Lyapunov approach along with classic mathematical tools such as Cauchy series, Parseval equality, and compact embeddings of Hilbert spaces.

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