Stability of nonlinear systems under constantly acting perturbations (Q1805118)

The paper deals with ``stability in terms of two measures'' of the unperturbed system of ODE \(\dot x= f(t, x)\). Stability is meant here not only with respect to initial values but also for perturbations of the right hand side: \(\dot x= f(t, x)+ R(t, x)\). The terms \((h_ 0, h, T_ 1)\) total stability, \((h_ 0, h, T_ 2)\) total stability and \((h_ 0, h)\) attractivity are defined where \(h_ 0\) and \(h\) are some positive scalar valued functions. Sufficient conditions are given for these stabilities in terms of Lyapunov functions. There are some misleading misprints the worst being the one in Theorem 3.1 (ii) where, probably \(V_{2.1}'\) is to be read. The conditions in Definitions 2.4 and 2.5 are not quite clear.