On the construction of ISS Lyapunov functions for networks of ISS systems
نویسندگان
چکیده
We consider a finite number of nonlinear systems interconnected in an arbitrary way. Under the assumption that each subsystem is input-to-state stable (ISS) regarding the states of the other subsystems as inputs we are looking for conditions that guarantee input-to-state stability of the overall system. To this end we aim to construct an ISS-Lyapunov function for the interconnection using the knowledge of ISS-Lyapunov functions of the subsystems in the network. Sufficient conditions of a small gain type are obtained under which an ISS Lyapunov function can be constructed. The ISS-Lyapunov function is then given explicitly, and guarantees that the network is ISS. Keywords— Nonlinear systems, Input-to-state stability, ISS Lyapunov function, small gain condition.
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