I often get the systems confused. Learned from MATH213.


Mathematically, a system is a map from a space of input signals to a space of output signals.

Notation 2

If represents some system then or or simply indicated that is the response (solution) of the system to the input signal .

Definition 4

A system is continuous-time (CT) if both its input and output signals are CT.

A system is discrete-time (FT) if both its input and output signals are DT. is a hybrid system if it contains both CT and DT signals.

Definition 4: Multivariable vs Scalar Systems

A system is multivariable if is has multiple inputs and/or outputs.

A system is scalar if it has a single input and a single output.


In thermodynamics terms:

  • An open system can exchange both energy and matter with its surroundings. The stovetop example would be an open system, because heat and water vapor can be lost to the air.
    • Energy is not conserved
  • A closed system can exchange only energy with its surroundings, not matter. If we put a very tightly fitting lid on the pot from the previous example, it would approximate a closed system.
  • An isolated system is one that cannot exchange either matter or energy with its surroundings. A perfect isolated system is hard to come by, but an insulated drink cooler with a lid is conceptually similar to a true isolated system. The items inside can exchange energy with each other, which is why the drinks get cold and the ice melts a little, but they exchange very little energy (heat) with the outside environment.