An overview of structural systems theory

This paper provides an overview of the research conducted in the context of structural (or structured) systems. These are parametrized models used to assess and design system theoretical properties without considering a specific realization of the parameters (which could be uncertain or unknown). The research in structural systems led to a principled approach to a variety of problems, into what is known as structural systems theory. Hereafter, we perform a systematic overview of the problems and methodologies used in structural systems theory since the latest survey by Dion et al. in 2003. During this period, most of the focus seems to be on structural system's properties related to controllability/observability and decentralized control, in the context of linear time-invariant systems, under the classic assumption that the parameters are independent and belonging to infinite fields. Notwithstanding, it is notable an increase in research in topics that go beyond such scope and underlying assumptions, as well as applications in a variety of domains. Lastly, we provide a compilation of open questions on several settings and we discuss future directions in this field.