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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.

##### MSC:
 34A37 Differential equations with impulses 34A30 Linear ODE and systems, general 34D20 Stability of ODE 37J25 Stability problems (finite-dimensional Hamiltonian etc. systems)
##### Keywords:
impulse; periodic system
Full Text:
##### References:
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