Continuous systems can be represented in the state-space form as:

x_c, is called the state of the system, and contains n elements for an nth-order system. In matrix notation, x_c is a column matrix of dimension nx1. u defines the inputs to the system. Its size is equal to the number of inputs to the system being modeled. In this description, the system is assumed to have m inputs, consequently u is a column matrix of size mx1. y defines the outputs from the system. If a system has p outputs, y is represented with a column matrix of dimension px1.

Using this system description, a nonlinear, second-order differential equation, with input u, such as:

can be written is state-space form as:

The state Equations 4 or 7a are integrated by ADAMS/Solver using its integrators. Therefore, it is necessary that the functional relationship expressed in Equations 4 or 7a be continuous. That is a minimum requirement for successfully integrating these equations. Similarly, if the output is to be fed back into a plant model, such as a mechanical system, Equations 5 or 7b are also required to be continuous. A higher degree of differentiability will help the integrators solve these equations more efficiently.