A Flat System Possessing no (x, u)-Flat Output

In general, flat outputs of a nonlinear system may depend on the system's state and input as well an arbitrary number time derivatives latter. If output which also depends is known, one pose question whether there exists independent these derivatives, i.e., (x,u)-flat output. Until now, every possesses has been open. this contribution, conjecture disproved by means counterexample. We present two-input differentially with depending state, first-order input, but does not possess any The proof relies fact that can be exactly linearized after at most dim(x)-fold prolongation its (new) inputs suitable transformation applied.