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Stability criteria for linear periodic impulsive Hamiltonian systems. (English) Zbl 1128.34005
The authors are concerned with the stability of linear impulsive Hamiltonian systems of the form: $$x'=a(t)x+b(t),\quad u'=-c(t)x-a(t)u,\quad t\ne \tau_i\tag1$$ $$x'=(\tau_i+)=\alpha_ix+(\tau_i-),\quad u(\tau_i+)=\alpha_iu(\tau_i-)-\beta_ix(\tau_i-1),\tag2$$ where $t\in\Bbb R$ and $i\in\Bbb Z$. Sufficient conditions for the stability of (1), (2) (all solutions are bounded on $\Bbb R$) are derived.

34A37Differential equations with impulses
34A30Linear ODE and systems, general
34D20Stability of ODE
37J25Stability problems (finite-dimensional Hamiltonian etc. systems)
Full Text: DOI
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[5] Krein, M. G.: Foundations of the theory of $\lambda $-zones of stability of canonical system of linear differential equations with periodic coefficients. In memory of A.A. Andronov. Amer. math. Soc. transl. Ser. 2, No. 120, 1-70 (1955)
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