Compositional Analysis for Linear Control Systems

The complexity of physical and engineering systems, both in terms of the governing physical phenomena and the number of subprocesses involved, is mirrored in ever more complex mathematical models. While the demand for precise models is indisputable, the analysis of such system models remains challenging. Adopting techniques from computer science makes available a framework for compositional analysis of interconnected control systems. Simulation relations relate process models with their specifications thus checking whether the derived model behaves as desired. Based on that, compositional and assume-guarantee reasoning rules decompose the actual verification task into several subtasks that can be checked with less computational effort. Thus, modularly composed system models can be treated with modular analysis techniques. In this paper, we want to give an overview of how these concepts can be applied to analyze linear continuous-time systems (LTI). Motivated by the underlying physics, we introduce a general type of interconnection that can also be interpreted as a feedback control configuration in the spirit of decentralized control. Additionally, parallel composition of LTI systems is discussed with special emphasis on decomposition strategies for a given specification. The proposed methodology could be extended further to classes of hybrid systems where compositional analysis techniques are of particular interest