| Abstract: | This paper deals with the free nonlinear dynamical system xdot](t)=A x(t)+h(t, x(t)), t≥t 0, x(t 0)=x 0, where A is an n×n-matrix and h a nonlinear vector function with h(t, u)=o(∥u∥). As the first novel point, a lower bound for the asymptotic behaviour on the solution x(t) is derived. Two methods are applied to determine the optimal two-sided bounds, where one of the methods is the differential calculus of norms. In this context, the second novel point enters; it consists of a new strategy to significantly reduce the computation time for the determination of the optimal constants in the two-sided bounds. The obtained results are especially of interest in engineering and cannot be obtained by the methods used so far. |
