Sentence examples for proven by using from inspiring English sources

(b) Unlike in the previous works, the stability analysis is rigorously proven by using a SPR-based Lypunov approach.

The finite-time stability nature of the TSMC law is proven by using a Lyapunov-based approach.

The control law was synthesized and stability of the controlled system was proven by using Lyapunov criterion.

The global stability and error convergence of the closed-loop system are proven by using the Lyapunov stability theorem.

Theoretically, its weak convergence is proven by using Markov theory, while the experimental results demonstrate its strong convergence.

The conjugate is also able to accommodate hydrophobic guests within the βCD cavity, as proven by using naphthalene as a model compound.

Stability and robustness are proved by using Lyapunov's method.

This result is proved by using the implicit function theorem.

The independence of the axioms is usually proved by using more than two truth values.

The asymptotic stability of the closed-loop MRR system is proved by using the Lyapunov theory.

Then, the stability of controlled system is proved by using Lyapunov's direct method.