Computer controlled systems are a foundation to today's society. Correctness of the functionality provided by these systems is of importance, since they are often deployed in safety-critical scenarios. Many of these systems include timed behavior. In order to ensure the quality of these systems, model-based design approaches can be employed where the systems under development are designed using models. The absence of erroneous behavior in these models can be ensured with formal methods. In this work, we use the modeling formalism of networks of timed automata. We approach two deficiencies of analysis techniques for these models. First, they easily run out of memory when exploring large, complex models. Second, they do not handle changes of the models efficiently. We provide a technique for the verification of safety properties specifying the absence of erroneous behavior for networks of timed automata. Our technique deliberately works distinct from other approaches in this field, as it employs induction and avoids explicit exploration and storage of states. In consequence, it is a valuable complement to existing technologies. Furthermore, in the presence of reconfigurations (i.e., changes) we reuse inductive invariants computed by our algorithm. This idea works well for a special class of systems, denoted Parameterized Timed Systems, where the number of timed automata is given as parameter. Our technique enables a verification of the entire system, irrespective of the actual number of automata. To this end, we verify the safety property for the smaller models of the family and reuse the computed inductive invariants to reason about the larger models. In addition, we examine the reusability of the inductive invariant for general models and reconfigurations.