Predicting adaptation for uncertain systems with robust real plots

In systems biology, perfect adaptation (adaptation) denotes the property of a system reacting to a step input stimulus by completely (partially) restoring the pre-stimulus output value at steady state. We address the problem of predicting adaptation for uncertain dynamical systems. To this aim, we introduce a formal definition of adaptation tailored to the robust analysis of dynamical systems. Whilst the definition is more general and valid also for the step response analysis of nonlinear systems, in the linear case such a definition of adaptation reduces to the presence of a single real zero that dominates all poles. Based on this definition, we can assess robust adaptation by means of the robust real plot, which characterises the position of real zeros and poles for linear systems with parametric uncertainties.