For deterministic discrete time systems, sequential inputs can be added by extending the update equation. If the dynamical system generates outputs, an output function is added as a system equation. While systems with no input are common, systems with no outputs have limited practicality.
| \( T \) | This is the symbol for a dynamical system's update operator. |
| \( \mathbf{x} \) | This symbol represents a state of the dynamical system at some time point. |
| \( O \) | This symbol represents the output function of a dynamical system. |
| \( \mathbf{u} \) | This symbol represents the input of a dynamical system. |
| \( \mathbf{y} \) | This symbol represents the output of a dynamical system. |
| \( n \) | This symbol represents any given whole number, \( n \in \htmlClass{sdt-0000000014}{\mathbb{W}}\). |
The symbol \( O \) represents a function that generates outputs of a dynamical system upon observing a particular state. This corresponds to a "measurement" of the system, often an appropriate analogy given the partial observability of real-life dynamical systems.