A **discrete system** is a system with a countable number of states. Discrete systems may be contrasted with continuous systems, which may also be called analog systems. A final discrete system is often modeled with a directed graph and is analyzed for correctness and complexity according to computational theory. Because discrete systems have a countable number of states, they may be described in precise mathematical models.

A computer is a finite state machine that may be viewed as a discrete system. Because computers are often used to model not only other discrete systems but continuous systems as well, methods have been developed to represent real-world continuous systems as discrete systems. One such method involves sampling a continuous signal at discrete time intervals.

References

*Hopcroft, John E.; Rajeev Motwani; Jeffrey D. Ullman (2001). Introduction to Automata Theory, Languages, and Computation (2nd ed.). Reading Mass: Addison-Wesley. ISBN 0-201-44124-1.**Benjamin C. Kuo (1995). Digital Control Systems (2nd ed.). USA: Oxford University Press. ISBN 0-19-512064-7.*