ABSTRACT
The notion of input-to-state stability (ISS) was introduced in [21]. Together with several variants, also discussed in this article, it provides theoretical concepts that describe various desirable stability features of a mapping u(·) → (·) from (time-dependent) inputs to outputs (or internal states). Prominent among these features are that inputs that are bounded, “eventually small,” “integrally small,” or convergent, should lead to outputs with the respective property. In addition, ISS and related notions quantify in what manner initial states affect transient behavior. The discussion in this article focuses on stability notions relative to globally attractive steady states, but a more general theory is also possible, that allows consideration of more arbitrary attractors, as well as robust and/or adaptive concepts. The reader is referred to the cited literature, as well as the textbooks [5,7,8,12,14,15,20], for extensions of the theory as well as applications, The paper [26] may also be consulted for further references and an exposition of many extensions of the concepts and results discussed in this chapter.
