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Input/output-to-state stability of nonlinear systems with average-delay impulses

This paper studies the input/output-to-state stability (IOSS) and integral IOSS (iIOSS) of nonlinear systems with delayed impulses. In order to address flexible delays in impulses, the method of average impulsive delay (AID) is used to describe such impulses, and it is said to be the average-delay impulses. Further, by using the method of average impulsive interval (AII), we propose some criteria for IOSS and iIOSS of the system with average-delay impulses. To be specific, a uniform relationship is established among the AII and AID constants, impulses, and the decay rate of the continuous dynamics such that IOSS and iIOSS of the system with average-delay impulses are guaranteed, respectively. Some illustrative examples are presented to show the validity of the obtained results.