Sentence examples for proved by using the from inspiring English sources

This result is proved by using the implicit function theorem.

The convergence of the identification error is proved by using the Lyapunov theory.

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

The uniform ultimate boundedness of the closed-loop system is also proved by using the Lyapunov approach.

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

Next, a corresponding theorem for nonlinear systems proved by using the Picard process in conjunction with the result for the linear case.

The FAT-based design is proposed here to estimate these uncertainties so that the closed-loop stability can be proved by using the Lyapunov-like theory.

Hence some safety properties concerning action scoping and concurrent exception handling can be proved by using the FDR (Failure Divergence Refinement) verification tool.

The constructed feedback control system is validated by published experimental data and its global asymptotic stability is proved by using the LaSalle's invariance principle.

Some properties of the problem are also investigated and proved by using the dynamic programming (DP) and two commonly used heuristics.

Stability of overall closed-loop system is rigorously proved by using the new convergence properties of a sequence of row stochastic matrices.