Flatness in systems theory is a system property that extends the notion of controllability from linear systems to nonlinear dynamical systems. A system that has the flatness property is called a flat system. Flat systems have a (fictitious) flat output, which can be used to explicitly express all states and inputs in terms of the flat output and a finite number of its derivatives. Flatness in systems theory is based on the mathematical notion of flatness in commutative algebra and is applied in control theory.