Superposition theorems for input-to-output stability of infinite dimensional systems

We characterize input-to-output stability of a general class of both continuous-time and discrete-time infinite dimensional systems in terms of weaker stability properties. Our results generalize the corresponding criteria for ordinary differential equations achieved by Ingalls et al. [1] and those for infinite dimensional systems for which the output equals the state [2]. This way, we investigate the relation between several stability and attractivity properties for infinite dimensional systems with outputs by providing the according implications and giving counterexamples, respectively.