Classification of systems

Continuous - Discrete

Continuous system: the input and output signals are continuous

Discrete system: the input and output signals are discrete

Linear - Nonlinear

Linear system: obeys the properties of scaling (homogeneity) and

superposition (additivity)

Nonlinear system: does not obeys either the property of scaling or

the property of superposition or both

Time invariant - Time variant

Time invariant system: does not depend on when it occurs (the shape of the output does not change with a delay of the input).

System S where S(x(t)) = y(t) is time invariant if for all T hold S(x(t-T)) = y(t-T)

When this property does not hold for a system, then it is said to be time variant or time varying

Causal - Noncausal

A causal system is one that is nonanticipative;

the output may depend on current and past inputs,

but not future inputs.

All "real-time" systems must be causal, since they can not have future inputs available to them

Example of an noncausal system:
image processing - the dependent variable might represent pixels to the left and right (the "future") of the current position on the image

Stable - Unstable

A stable system is one where the output does not diverge as long as the input does not diverge.
A bounded input produces a bounded output. (also referred to as bounded input-bounded output (BIBO) stable)

In an unstable system, the output grows without limit (diverges) from a bounded input