Abstract
Input-to-state stability (ISS), integral-ISS (iISS) and their related notions of input/output stability and detectability have become a useful framework for nonlinear feedback analysis and design. In this paper, a new notion, that of constrained input-to-state stability (cISS), is presented and several characterizations of cISS are obtained. cISS, unlike ISS or iISS, is not confined to forward complete systems and generalizes the small-signal L∞ stability. Moreover, for a class of nonlinear systems, constrained input-to-state stabilizability implies the solvability of an inverse optimal problem. The paper shows that cISS is a natural concept to improve the ISS framework.
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