In this paper we give an overview of results on the analysis of parametric linear hybrid automata, and of systems of similar linear hybrid automata: We consider, for instance, systems with a parametric (i.e. not explicitly specified) number of similar components, which can be connected to other systems, and in which the properties of some function symbols might be underspecified, and global safety properties which can be expressed by universally quantified first-order formulae, using quantification over variables ranging over the component systems. After presenting a possibility of describing such systems, we analyze possibilities of using methods for hierarchical reasoning and symbol elimination for determining relationships on (some of) the parameters used in the description of these systems under which the global safety properties are guaranteed to be inductive invariants. We discuss an implementation and illustrate its use on several examples.