connects changes of $\mu$ to current values of $\mu$. This represents the behavior of a hybrid system. Special cases of Eq. can be linked to the previously presented methods of modeling hybrid systems. Choosing $$\dot{\mu} = g(t)$$ results in the formulation of SARX models (see \[SARX\]). In cases where the change of the qualitative behavior of the system depends on only current values of the state $x$, the change of $\mu$ can be represented by $$\dot{\mu} = g(x(t)), \label{eq:MuDerivativePWARX}$$ which is the premise of PieceWise-Affine (PWA) models (see \[PWARX\]). For a linear function $g$, the regions for each state have a linear border. For a nonlinear $g$, complex borders can be modeled between regions, as is the case for NPWA models. If the function $f$ in Eq. is linear, the formulation is equivalent to PWARX models, otherwise it results in PWNARX models.\
Hysteresis models not only depend on the current state of the system, but also on past values up to a horizon $q$. Let $$\dot{\mu} = g(x(t-q), x(t-q+1), ..., x(t-1), x(t), \mu) = g(x_q, \mu).$$ This way, $\mu(t)$ serves as a storage for information of past values of the system. The general formulation Eq. is equivalent to $$\dot{\mu} = 