  Assessment of the degree of boundedness/stability of multidimensional
nonlinear systems with time-dependent and nonperiodic coefficients is an
important problem in various applied areas which has no adequate resolution
yet. Most of the known techniques provide computationally intensive and
conservative stability criteria in this field and frequently fail to estimate
the regions of boundedness/stability of solutions to the corresponding systems.
Recently, we outlined a new approach to this problem which is based on the
analysis of solutions to a scalar auxiliary equation bounded from the above
time histories of the norms of solutions to the original system. This paper
develops a novel technique casting the auxiliary equation in a modified form
which extends the application domain and reduces the computational hamper of
our prior approach. Consequently, we developed more general
boundedness/stability criteria and estimated trapping/stability regions for
some multidimensional nonlinear systems with nonperiodic time-dependent
coefficients that are common in various application domains. This let us to
assess in target simulations the extent of boundedness/stability of some
multidimensional, nonlinear and time-varying systems which were intractable
with our prior technique.
