Lyapunov inequalities and stability for linear Hamiltonian systems (Q649760)
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scientific article; zbMATH DE number 5986516
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Lyapunov inequalities and stability for linear Hamiltonian systems |
scientific article; zbMATH DE number 5986516 |
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Lyapunov inequalities and stability for linear Hamiltonian systems (English)
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6 December 2011
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The paper considers qualitative properties of the Hamiltonian system \[ Ju' = H(t)u ,\quad u=\mathrm{col}(x^T\;y^T)\in \mathbb R^n \] expressed via various Lyapunov-like inequalities. Discussed are the standard boundary value problem \[ x(a) = x(b) = 0 \] and its applications to quantum mechanics. The paper ends with some stability criteria for planar Hamiltonian systems. All results can be seen as either improvements or generalizations of Lyapunov inequalities.
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linear Hamiltonian system
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Lyapunov inequality
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eigenvalue
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stability
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