  The differential equations with piecewise constant argument (DEPCAs, for
short) is a class of hybrid dynamical systems (combining continuous and
discrete). In this paper, under the assumption that the nonlinear term is
partially unbounded, we study the bounded solution and global topological
linearisation of a class of DEPCAs of general type. One of the purpose of this
paper is to obtain a new criterion for the existence of a unique bounded
solution, which improved the previous results. The other aim of this paper is
to establish a generalized Grobman-Hartman-type theorem for the topological
conjugacy between a nonlinear perturbation system and its linear system. The
method is based on the new obtained criterion for bounded solution. The
obtained results generalized and improved some previous papers. Some novel
techniques are employed.
