Asymptotic stability of solutions of systems with impulsive action (Q799854)

A linear variable parameter system with impulse perturbation \(\dot x=A(t)x+F(x,t)\), \(x(t)\in R^ n\), is considered. With some axioms upon the \(n\times n\) matrix A, the linear system \(\dot x=A(t)x\) is shown to be stable and some estimates for its solutions are brought about. Then the same result is obtained for the full system with specified estimates on the impulse f(x,t).