Provide several concepts of general input-to-state stability for the nonlinear delay systems. That is generalized globally exponential integral input-to-state stability (GGE-iISS), generalized globally integral exponential integral input-to-state stability (GGIE-iISS), and eλt -weighted generalized globally integral exponential integral input-to-state stability ( eλt -weighted GGIE-iISS).
Give out the stability conditions of the general input-to-state stability for the nonlinear delay systems. Moreover, strict theoretical derivation is given to prove the sufficiency and correctness of the given conditions.
An example is given to illustrate the correctness of the obtained theoretical results.