LTI Models (Creating and Manipulating Models)

Creating and Manipulating Models

Model-Specific Properties

The remaining LTI properties are specific to one of the four model types (TF, ZPK, SS, or FRD). For single LTI models, these are summarized in the following four tables. The property values differ for LTI arrays. See set for more information on these values.

Table 1-5: TF-Specific Properties
Property Name
Description
Property Value

den
Denominator(s)
Real cell array of row vectors

num
Numerator(s)
Real cell array of row vectors

Variable
Transfer function variable
String 's', 'p', 'z', 'q', or 'z^-1'

Table 1-6: ZPK-Specific Properties
Property Name
Description
Property Value

k
Gains
Two-dimensional real matrix

p
Poles
Cell array of column vectors

Variable
Transfer function variable
String 's', 'p', 'z', 'q', or 'z^-1'

z
Zeros
Cell array of column vectors

Table 1-7: SS-Specific Properties
Property Name
Description
Property Value

a
State matrix
2-D real matrix

b
Input-to-state matrix
2-D real matrix

c
State-to-output matrix
2-D real matrix

d
Feedthrough matrix
2-D real matrix

e
Descriptor matrix
2-D real matrix

Nx
Number of states
Scalar integer

StateName
State names
Cell vector of strings

**Table 1-5: TF-Specific Properties**
Property Name	Description	Property Value
`den`	Denominator(s)	Real cell array of row vectors
`num`	Numerator(s)	Real cell array of row vectors
`Variable`	Transfer function variable	String `'s'`, `'p'`, `'z'`, `'q'`, or `'z^-1'`

**Table 1-6: ZPK-Specific Properties**
Property Name	Description	Property Value
`k`	Gains	Two-dimensional real matrix
`p`	Poles	Cell array of column vectors
`Variable`	Transfer function variable	String `'s'`, `'p'`, `'z'`, `'q'`, or `'z^-1'`
`z`	Zeros	Cell array of column vectors

**Table 1-7: SS-Specific Properties**
Property Name	Description	Property Value
`a`	State matrix	2-D real matrix
`b`	Input-to-state matrix	2-D real matrix
`c`	State-to-output matrix	2-D real matrix
`d`	Feedthrough matrix	2-D real matrix
`e`	Descriptor matrix	2-D real matrix
`Nx`	Number of states	Scalar integer
`StateName`	State names	Cell vector of strings

Table 1-8: FRD-Specific Properties
Property Name
Description
Property Value

Frequency
Frequency data points
Real-valued vector

ResponseData
Frequency response
Complex-valued multidimensional array

Units
Units for frequency
String 'rad/s' or 'Hz'

**Table 1-8: FRD-Specific Properties**
Property Name	Description	Property Value
`Frequency`	Frequency data points	Real-valued vector
`ResponseData`	Frequency response	Complex-valued multidimensional array
`Units`	Units for frequency	String `'rad/s'` or `'Hz'`

Most of these properties are dedicated to storing the model data. Note that the matrix is set to [] (the empty matrix) for standard state-space models, a storage-efficient shorthand for the true value .

The Variable property is only an attribute of TF and ZPK objects. This property defines the frequency variable of transfer functions. The default values are 's' (Laplace variable ) in continuous time and 'z' (Z-transform variable ) in discrete time. Alternative choices include 'p' (equivalent to ) and 'q' or 'z^-1' for the reciprocal of the variable. The influence of the variable choice is mostly limited to the display of TF or ZPK models. One exception is the specification of discrete-time transfer functions with tf (see tf for details).

Note that tf produces the same result as filt when the Variable property is set to 'z^-1' or 'q'.

Finally, the StateName property is analogous to the InputName and OutputName properties and keeps track of the state names in state-space models.

Generic Properties Setting LTI Properties