Sentence examples for are proved by using from inspiring English sources

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

The global stability and the convergence of the designed controller are proved by using Lyapunov method.

Moreover, in the absence of lumped disturbance input, asymptotical convergence of relative pose are proved by using the Lyapunov method.

Moreover, the uniform ultimate boundedness of the weights of the identifier NN and the critic NN are proved by using Lyapunov's direct method.

The local and global existence theorems under different conditions are proved by using selection theorems and Kakutani's fixed point theorem.

The existence and uniqueness of solutions for the system are proved by using the Banach fixed point theorem.

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

Hence the existence and uniqueness of this theorem are proven by using Lemma 2.3 with λ = 1.

This result is proved by using the implicit function theorem.

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.