On Incremental Input-to-State Stability of interconnected discrete-time systems

In this technical communique, the properties of interconnected Incrementally Input-to-State Stable (δISS) discrete-time systems are studied. In particular, a small gain theorem for δISS systems with feedback connection is derived with two formulations: one based on the definition of δISS, and one based on δISS-Lyapunov functions.