A tool for stability analysis of nonlinear large-scale systems by cascading star products

This paper proposes a new tool for establishing input-to-state stability (ISS) of nonlinear interconnected systems. The cascade of Redheffer´s star products is spotlighted as a geometrical arrangement of interconnection by which a broad class of nonlinear large-scale systems can be treated effectively in a unified manner. The new stability theorem this paper proposes imposes conditions on supply rates of individual subsystems separately. One of good features is that the conditions do not rely on recursive augmentation of subsystems, so that recursive calculation of the stability conditions are not needed and the proposed stability criterion is free from propagation of complexity. The idea of scaling supply rates renders the criterion not only simple, but also applicable to uncertain systems