A Small-Gain Theorem in the Absence of Strong iISS

Previous small-gain results for interconnected integral input-to-state (iISS) systems have been restricted to systems that are strongly iISS. This paper removes this restriction by allowing cross terms between external inputs and states in the Lyapunov decrease of component systems, and subsequently constructing a nonseparable Lyapunov function. An example demonstrates the use of this new small-gain formulation.