The analysis and design of nonlinear feedback systems has recently undergone an exceptionally rich period of progress and
maturation, fueled, to a great extent, by (1) the discovery of certain basic conceptual notions, and (2) the identification
of classes of systems for which systematic decomposition approaches can result in effective and easily computable control
laws. These two aspects are complementary, since the latter approaches are, typically, based upon the inductive verification
of the validity of the former system properties under compositions (in the terminology used in [62], the “activation” of theoretical
concepts leads to “constructive” control).
This expository presentation addresses the first of these aspects, and in particular the precise formulation of questions
of robustness with respect to disturbances, formulated in the paradigm of input to state stability. We provide an intuitive and informal presentation of the main concepts. More precise statements, especially about older
results, are given in the cited papers, as well as in several previous surveys such as [103, 105] (of which the present paper
represents an update), but we provide a little more detail about relatively recent work. Regarding applications and extensions
of the basic framework, we give some pointers to the literature, but we do not focus on feedback design and specific engineering
problems; for the latter we refer the reader to textbooks such as [27, 43, 44, 58, 60, 66, 96].