Small gain theorems for networks of heterogeneous systems

摘要

We prove a small-gain theorem for interconnections ofnnonlinear heterogeneous input-to-state stable control systems of a general nature, covering partial, delay and ordinary differential equations. We use in this paper the summation formulation of the ISS property, but the method can be adapted to other formulations of the ISS concept as well. The proof is based on the recent characterizations of the input-to-state stability for infinite-dimensional systems in terms of weaker stability properties.