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This article presents a formal study of the transient stabilization problem, including a stability proof.
It also provides an implicit stability proof.
A rigorous mathematical stability proof is given.
The stability Proof of the closed-loop system is presented.
The stability is guaranteed by using a rigid stability proof.
A rigorous stability proof is provided under certain assumptions.
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The stability proofs also give the possible feedback gains which achieve stabilization.
Using applied conditions and stability proofs, we find that the proposed control design procedure is simplified.
Formal nonlinear stability proofs are given to show that the tracking error is small.
The convergence and stability proofs are derived in the port Hamiltonian framework.
By using the Lyapunov theory, rigorous stability proofs for the closed-loop system are presented.
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