Stability criteria for linear periodic Hamiltonian systems (Q961105)

Consider the first order linear system \[ x^{\prime }=a(t)x+b(t)u,\quad u^{\prime }=-c(t)x-a(t)u,\quad t\in \mathbb R,\tag{\(*\)} \] where \(a,b\) and \(c\) are \(T\)-periodic real-valued piece-wise continuous functions defined on \(\mathbb R\). The system (\(*\)) is said to be stable if all solutions are bounded on \(\mathbb R\), unstable if all nontrivial solutions are unbounded on \(\mathbb R\), and conditionally stable if there exists a nontrivial solution bounded on \(\mathbb R\). The author obtain new stability criteria for (\(*\)).