Sufficient conditions for asymptotic stability of linear autonomous impulsive systems (Q1293540)

The author investigates the asymptotic stability of a linear system of differential equations with impulses \[ x'(t)=Ax(t),\quad t\neq t_{k},\;t\geq t_{0} \qquad \quad x(t_{k}^{+})=C x(t_{k}), \] where \(A\) and \(C\) are constant \((n\times n)\)-matrices, \(C\) invertible. In the particular case when \(A\) and \(C\) are diagonalizable, an easily verifiable condition is given to assure the asymptotic stability of the system. For the general situation, a sufficient condition is proved by using the method of quasidiagonalization. Two interesting examples are worked out to illustrate the applicability of the main results and to discuss some relevant facts about remarkable aspects of such results.