Generalized exponential input-to-state stability of nonlinear systems with time delay☆

Abstract This paper studies the general input-to-state stability problem of the nonlinear delay systems. By employing Lypaunov–Razumikhin technique, several general input-to-state stability concepts, that is generalized globally exponential integral input-to-state stability (GGE-iISS), generalized globally integral exponential integral input-to-state stability (GGIE-iISS), and e λt -weighted generalized globally integral exponential integral input-to-state stability ( e λt -weighted GGIE-iISS) are studied. An example is given to illustrate the correctness of the obtained theoretical results.