Non-conservative dissipativity and small-gain theory for ISS networks

This paper addresses input-to-state stability (ISS) analysis for discrete-time systems using the notion of finite-step ISS Lyapunov functions. Here, finite-step Lyapunov functions are energy functions that decay after a fixed but finite number of steps, rather than at every time step. We establish non-conservative dissipativity and small-gain conditions for ISS of networks of discrete-time systems, by generalizing results in [1] and [2] to the case of ISS. The effectiveness of the results is illustrated through two examples.