# Transmission system

A transmission system (often just short system ) is in the system theory , a mathematical model of a process that a signal converts and transmits. The signal supplied is called the input signal and the resulting converted signal is called the output signal . The way in which the signal is converted or how these two signals are related to one another is described by the transfer function.

## Single-size and multi-size systems

A transmission system that has only one input and one output is called a single- variable system or SISO system (from English single input, single output )

If the system has several inputs and outputs, one speaks of a multi-variable system or MIMO system (from English multiple input, multiple output ).

The SIMO systems (from single input, multiple output ) with one input and several outputs still exist as a mixed form . And vice versa, MISO systems (from multiple input, single output with multiple inputs and only one output).

## Dynamic and static systems

• static: The value of the output signal y (t) depends at any point in time t only on the current value of the input signal u (t). (algebraic description)
• dynamic: The output signal depends on previous input signals. (Description using differential equations)

## Systems with concentrated and distributed parameters

• concentrated parameters: effect arrangements with location-independent signals (description by means of ordinary differential equations)
• distributed parameters: effect arrangements with position-dependent signals (description using partial differential equations)

## Linear and non-linear systems

A system is called linear if the following two conditions are met:

• Reinforcement principle: ${\ displaystyle f (k \ cdot u (t)) = k \ cdot f (u (t))}$
• Overlay principle: ${\ displaystyle f \ left (u_ {1} \ left (t \ right) \ right) + f \ left (u_ {2} \ left (t \ right) \ right) = f \ left (u_ {1} \ left (t \ right) + u_ {2} \ left (t \ right) \ right)}$

If either or both of these conditions are not met, the system is said to be non-linear.

## Time-variable and time-invariant systems

• time-variable: system parameters change over time (e.g. mass of a rocket). Adaptive controllers are necessary to influence such systems.
• time-invariant: systems with constant system parameters.

## Systems with continuous and time-discrete signals

For processing by computers, continuous signals from physical systems are converted into time-discrete signals. This system is called the scanning system.