The Small-Gain Theorem for Nonlinear Systems and Its Applications to Robust Stability

  • Alberto IsidoriEmail author
Part of the Advanced Textbooks in Control and Signal Processing book series (C&SP)


As it is the case for linear systems, understanding the influence of interconnections on stability and asymptotic behavior is of paramount importance. In the case of nonlinear systems, a powerful concept in the analysis of interconnections is the notion of gain function of an input-to-state stable system. Using this concept, it is possible to develop a nonlinear version of the small-gain theorem, which is useful in the analysis as well as in the design of feedback laws. This chapter describes this theorem and how it can be used in the design of stabilizing feedback laws for nonlinear systems.


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© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Dipartimento di Ingegneria Informatica, Automatica e GestionaleUniversità degli Studi di Roma “La Sapienza”RomeItaly

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