@@ -9,6 +9,97 @@ Library conventions
99The python-control library uses a set of standard conventions for the way
1010that different types of standard information used by the library.
1111
12+ LTI system representation
13+ =========================
14+
15+ Linear time invariant (LTI) systems are represented in python-control in
16+ state space, transfer function, or frequency response data (FRD) form. Most
17+ functions in the toolbox will operate on any of these data types and
18+ functions for convering between between compatible types is provided.
19+
20+ State space systems
21+ -------------------
22+ The :class: `StateSpace ` class is used to represent state-space realizations
23+ of linear time-invariant (LTI) systems:
24+
25+ .. math ::
26+
27+ \frac {dx}{dt} &= A x + B u \\
28+ y &= C x + D u
29+
30+
31+
32+ To create a state space system, use the :class: `StateSpace ` constructor:
33+
34+ sys = StateSpace(A, B, C, D)
35+
36+ State space systems can be manipulated using standard arithmetic operations
37+ as well as the :func: `feedback `, :func: `parallel `, and :func: `series `
38+ function. A full list of functions can be found in :ref: `function-ref `.
39+
40+ Transfer functions
41+ ------------------
42+ The :class: `TransferFunction ` class is used to represent input/output
43+ transfer functions
44+
45+ .. math ::
46+
47+ G(s) = \frac {\text {num}(s)}{\text {den(s)}}
48+ = \frac {a_0 s^n + a_1 s^{n-1 } + \cdots + a_n}
49+ {b_0 s^m + b_1 s^{m-1 } + \cdots + b_m},
50+
51+
52+
53+ To create a transfer function, use the :class: `TransferFunction `
54+ constructor:
55+
56+ sys = TransferFunction(num, den)
57+
58+ Transfer functions can be manipulated using standard arithmetic operations
59+ as well as the :func: `feedback `, :func: `parallel `, and :func: `series `
60+ function. A full list of functions can be found in :ref: `function-ref `.
61+
62+ FRD (frequency response data) systems
63+ -------------------------------------
64+ The :class: `FRD ` class is used to represent systems in frequency response
65+ data form.
66+
67+ The main data members are `omega ` and `fresp `, where `omega ` is a 1D array
68+ with the frequency points of the response, and `fresp ` is a 3D array, with
69+ the first dimension corresponding to the output index of the FRD, the second
70+ dimension corresponding to the input index, and the 3rd dimension
71+ corresponding to the frequency points in omega.
72+
73+ FRD systems have a somewhat more limited set of functions that are
74+ available, although all of the standard algebraic manipulations can be
75+ performed.
76+
77+ Discrete time systems
78+ ---------------------
79+ By default, all systems are considered to be continuous time systems. A
80+ discrete time system is created by specifying the 'time base' dt. The time
81+ base argument can be given when a system is constructed:
82+
83+ * dt = None: continuous time
84+ * dt = number: discrete time system with sampling period 'dt'
85+ * dt = True: discrete time with unspecified sampling period
86+
87+ Only the :class: `StateSpace ` and :class: `TransferFunction ` classes allow
88+ explicit representation of discrete time systems.
89+
90+ Systems must have the same time base in order to be combined. For
91+ continuous time systems, the :func: `sample_system ` function or the
92+ :meth: `StateSpace.sample ` and :meth: `TransferFunction.sample ` methods can be
93+ used to create a discrete time system from a continuous time system. See
94+ :ref: `utility-and-conversions `.
95+
96+ Conversion between representations
97+ ----------------------------------
98+ LTI systems can be converted between representations either by calling the
99+ constructor for the desired data type using the original system as the sole
100+ argument or using the explict conversion functions :func: `ss2tf ` and
101+ :func: `tf2ss `.
102+
12103.. _time-series-convention :
13104
14105Time series data
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