Any software bug or device malfunction in safety-critical systems can have catastrophic consequences. The validation and analysis of programs in critical systems is of paramount importance to guarantee that the software satisfies its specification and that it is devoided of runtime errors. Static program analysis by abstract interpretation computes a sound approximation of the set of reachable states of a program. It discovers invariant properties of programs which are represented by elements of an abstract domain. Most industrial static analysis tools do not use expressive relational numerical abstract domains like convex polyhedra due to their computational cost. We propose a new modular analysis for the automatic discovery of numerical properties based on the computation of disjunctive relational summaries of procedures. Procedure summaries are computed once and for all, and used to compute the effect of procedure calls, in a bottom-up fashion. Our approach is especially applied to improve the scalability of Linear Relation Analysis, or abstract interpretation with convex polyhedra, although it is based on a more general framework usable with any relational abstract domain. Disjunctive relational summaries are finite sets of abstract input-output relations represented by elements of a relational abstract domain. They are computed based on a partitioning of procedure preconditions. We give heuristics to compute an abstract partition of a procedure precondition. We also give ways to improve the precision of summary computation, notably through a careful treatment of preconditions during analysis. Our approach also applies to recursive procedures where summaries are computed recursively in terms of themselves. We implemented our approach in a new static analysis platform for C programs called mars. We conducted experiments on programs from the Mälardalen benchmark showing that our approach can significantly reduce the analysis time for Linear Relation Analysis compared to a full context-sensitive analysis where procedures are analyzed completely in each call context. Analysis precision is not significantly damaged and can even be improved due to the use of disjunction. In a second part, we present an approach for the modular analysis of reactive systems for numerical properties. We propose a flexible representation of the behavior of reactive components called Relational Mode Automata (RMA), which allows the analysis of reactive systems behavior at various levels of abstraction. RMA can be constructed automatically from disjunctive summaries of the procedures implementing component reactions. The analysis results of individual components using RMA can be reused to analyze larger reactive systems with multiple component instantiations in a modular way. We give an application of this approach to the analysis of a simplified automated subway control system.