Supplemental material to: Dynamics and Stability of a Class of Low Reynolds Number Swimmers Near a Wall

where u ∈ IR are the inputs and u ∈ IR are the outputs of the system. Traditionally, in a control problem, one needs to design input functions u = u(t), or a feedback law u = u(x, t), which is based on measuring the state variables x in real-time, in order to obtain a desired motion of the output functions y(t) under (2), for tasks such as tracking a desired trajectory or stabilization of an equilibrium point. Under a given input u = u(x, t), substituting into (2) and ignoring the output y, one again obtains a dynamical system of the form (1), where notions such as equilibrium points and their stability can then be studied.