System

Learned from MATH213.

System

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

Notation 2 (Response)

If $S$ represents some system then $f\to y$ or $y(t)=(Sf)(t)$ or simply $y=Sf$ indicates that $y(t)$ is the response (solution) of the system $S$ to the input signal $f(t)$.

Definition 4

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

A system $S$ is discrete-time (FT) if both its input and output signals are DT. $S$ 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.

Thermodynamics

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.
  • $\Delta E_{system}=0$
• 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.

Related

• Signal
• LTI