Some results on sensitivity and robust stability of input-output systems governed by integral and differential equations

We consider input-output systems (not necessarily of feedback type) on the time domain [0, ) which are governed by nonlinear vector integral or differential equations that relate the input and the output. Assuming that these equations depend on a parameterA, describing perturbations, which is allowed to vary in a vicinity of a nominal valueA₀ in a linear space, we study how strongly the output is affected by changes of (a)A₀ when the input is fixed (insensitivity), and (b) the input whenA is fixed withAA₀ being not too large (robust stability).The results are based on the theory of input-output systems over abstract extended spaces given in Parts I and II of [3]. We discuss nominal systems described by nonlinear Volterra and differential equations, and consider two types of possible perturbations. We also prove a simple result on systems governed by singular differential equations whose perturbations can change the order of the system.