Stability criteria for linear periodic impulsive Hamiltonian systems (Q2642180)

The authors are concerned with the stability of linear impulsive Hamiltonian systems of the form: \[ x'=a(t)x+b(t),\quad u'=-c(t)x-a(t)u,\quad t\neq \tau_i\tag{1} \] \[ x'=(\tau_i+)=\alpha_ix+(\tau_i-),\quad u(\tau_i+)=\alpha_iu(\tau_i-)-\beta_ix(\tau_i-1),\tag{2} \] where \(t\in\mathbb R\) and \(i\in\mathbb Z\). Sufficient conditions for the stability of (1), (2) (all solutions are bounded on \(\mathbb R\)) are derived.