.. math::

G(s) = \frac{\text{num}(s)}{\text{den}(s)}

= \frac{a_0 s^n + a_1 s^{n-1} + \cdots + a_n}

{b_0 s^m + b_1 s^{m-1} + \cdots + b_m},

= \frac{a_0 s^m + a_1 s^{m-1} + \cdots + a_m}

{b_0 s^n + b_1 s^{n-1} + \cdots + b_n},

where n is generally greater than or equal to m (for a proper transfer

function).

Discrete time systems

---------------------

By default, all systems are considered to be continuous time systems. A

discrete time system is created by specifying the 'time base' dt. The time

base argument can be given when a system is constructed:

A discrete time system is created by specifying a nonzero 'timebase', dt.

The timebase argument can be given when a system is constructed:

* dt = None: no timebase specified

* dt = None: no timebase specified (default)

* dt = 0: continuous time system

* dt > 0: discrete time system with sampling period 'dt'

* dt = True: discrete time with unspecified sampling period

Only the :class:`StateSpace` and :class:`TransferFunction` classes allow

explicit representation of discrete time systems.

Systems must have the same time base in order to be combined. For

continuous time systems, the :func:`sample_system` function or the

:meth:`StateSpace.sample` and :meth:`TransferFunction.sample` methods can be

used to create a discrete time system from a continuous time system. See

:ref:`utility-and-conversions`.

Systems must have compatible timebases in order to be combined. A system

with timebase `None` can be combined with a system having a specified

timebase; the result will have the timebase of the latter system.

Similarly, a discrete time system with unspecified sampling time (`dt =

True`) can be combined with a system having a specified sampling time;

the result will be a discrete time system with the sample time of the latter

system. For continuous time systems, the :func:`sample_system` function or

the :meth:`StateSpace.sample` and :meth:`TransferFunction.sample` methods

can be used to create a discrete time system from a continuous time system.

See :ref:`utility-and-conversions`.

Conversion between representations

----------------------------------

Time series data

================

This is a convention for function arguments and return values that

represent time series: sequences of values that change over time. It

is used throughout the library, for example in the functions

A variety of functions in the library return time series data: sequences of

values that change over time. A common set of conventions is used for

returning such data: columns represent different points in time, rows are

different components (e.g., inputs, outputs or states). For return

arguments, an array of times is given as the first returned argument,

followed by one or more arrays of variable values. This convention is used

throughout the library, for example in the functions

:func:`forced_response`, :func:`step_response`, :func:`impulse_response`,

and :func:`initial_response`.

.. note::

This convention is different from the convention used in the library

:mod:`scipy.signal`. In Scipy's convention the meaning of rows and columns

is interchanged. Thus, all 2D values must be transposed when they are

used with functions from :mod:`scipy.signal`.

The convention used by python-control is different from the convention

used in the `scipy.signal

<https://docs.scipy.org/doc/scipy/reference/signal.html>`_ library. In

Scipy's convention the meaning of rows and columns is interchanged.

Thus, all 2D values must be transposed when they are used with functions

from `scipy.signal`_.

Types:

plots to be set as dB for gain, degrees for phase and Hertz for frequency

(MATLAB conventions) or the gain can be given in magnitude units (powers of

10), corresponding to the conventions used in `Feedback Systems

<http://www.cds.caltech.edu/~murray/FBSwiki>`_.

<http://fbsbook.org>`_ (FBS).

Variables that can be configured, along with their default values:

* bode_dB (False): Bode plot magnitude plotted in dB (otherwise powers of 10)

Functions that can be used to set standard configurations:

.. autosummary::

:toctree: generated/

use_fbs_defaults

use_matlab_defaults