Improved small gain conditions for input-to-state stability with respect to measurement functions: Discrete time networked system

In this paper we study input-to-state stability with respect to measurement functions for discrete time networked systems. In such a networked system, the trajectory of each subsystem is affected by another in each time step, and this constraining system may change from step to step. We derive small gain conditions of input-to-state stability with respect to measurement functions for this type of discrete time networked system relying on the construction of dissipative-form finite time Lyapunov function. These conditions loosen those presented in [1] and [2]. Finally, we demonstrate the applicability of our results by applying them to the stability analysis of a distributed graph algorithm which does not satisfy the conditions of [1] and [2].