A small gain condition for interconnections of ISS systems with mixed\n ISS characterizations

2010/06/11 by Sergey Dashkovskiy, Dashkovskiy, Sergey, Michael Kosmykov +3
Engineering · Mathematics · #Control and Stability of Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Stability and Control of Uncertain Systems #Wireless Power Transfer Systems #math.DS

paper · pdf · doi:10.48550/arxiv.1006.2360

arxiv created 2010/06/11 · openalex publication_date 2010/06/11 · arxiv updated 2010/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider interconnected nonlinear systems with external inputs, where each\nof the subsystems is assumed to be input-to-state stable (ISS). Sufficient\nconditions of small gain type are provided guaranteeing that the\ninterconnection is ISS with respect to the external input. To this end we\nextend recently obtained small gain theorems to a more general type of\ninterconnections. The small gain theorem provided here is applicable to\nsituations where the ISS conditions are formulated differently for each\nsubsystem and are either given in the maximization or the summation sense.\nFurthermore it is shown that the conditions are compatible in the sense that it\nis always possible to transform sum formulations to maximum formulations\nwithout destroying a given small gain condition. An example shows the\nadvantages of our results in comparison with the known ones.\n

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