There are many systems that are neither continuous nor discrete. Some signals are sampled at discrete intervals, while others are sampled continuously. These systems are called sample data systems and are represented in the state-space form as:

Equations 10 represent the dynamics associated with the continuous piece of the sampled system. States x_c are continuous and fc() is assumed to be continuous.

Equations 11 represent the dynamics associated with the discrete piece of the sampled system. The equations are evaluated only at discrete points in time, the sample times for the sampled system. In between sample times, the discrete states are assumed to be constant.

Equation 12 defines the outputs of the system. It is important to note that the ADAMS integrators evaluate Equation 12 as often as necessary. In many problems, it is important to examine the output between sampling instants. Often, for example, the maximum overshoot may occur not at a sampling point, but between samples. This implementation allows for such observations to be made on the output.