This thesis is dedicated to the analysis of low-level software, like operating systems, by abstract interpretation. Analyzing OSes is a crucial issue to guarantee the safety of software systems since they are the layer immediately above the hardware and that all applicative tasks rely on them. For critical applications, we want to prove that the OS does not crash, and that it ensures the isolation of programs, so that an untrusted program cannot disrupt a trusted one. The analysis of this kind of programs raises specific issues. This is because OSes must control hardware using instructions that are meaningless in ordinary programs. In addition, because hardware features are outside the scope of C, source code includes assembly blocks mixed with C code. These are the two main axes in this thesis: handling mixed C and assembly, and precise abstraction of instructions that are specific to low-level software. This work is motivated by the analysis of a case study emanating from an industrial partner, which required the implementation of proposed methods in the static analyzer Astrée. The first part is about the formalization of a language mixing simplified models of C and assembly, from syntax to semantics. This specification is crucial to define what is legal and what is a bug, while taking into account the intricacy of interactions of C and assembly, in terms of data flow and control flow. The second part is a short introduction to abstract interpretation focusing on what is useful thereafter. The third part proposes an abstraction of the semantics of mixed C and assembly. This is actually a series of parametric abstractions handling each aspect of the semantics. The fourth part is interested in the question of the abstraction of instructions specific to low-level software. Interest properties can easily be proven using ghost variables, but because of technical reasons, it is difficult to design a reduced product of abstract domains that allows a satisfactory handling of ghost variables. This part builds such a general framework with domains that allow us to solve our problem and many others. The final part details properties to prove in order to guarantee isolation of programs that have not been treated since they raise many complicated questions. We also give some suggestions to improve the product of domains with ghost variables introduced in the previous part, in terms of features and performances.