Documentation 
Statespace model with identifiable parameters
sys = idss(A,B,C,D) creates a statespace model with identifiable parameters. A, B, C, and D are the initial values of the statespace matrices. By default, sys is discretetime model with unspecified sampling time and no state disturbance element.
sys = idss(A,B,C,D,K,x0) creates a statespace model with initial state values given by the vector x0.
sys = idss(A,B,C,D,K,x0,Ts) creates a statespace model with sampling time Ts. Use Ts = 0 to create a continuoustime model.
sys = idss(___,Name,Value) creates a statespace model using additional options specified by one or more Name,Value pair arguments.
sys = idss(sys0) converts any dynamic system model, sys0, to idss model form.
An idss model represents a system as a continuoustime or discretetime statespace model with identifiable (estimable) coefficients.
A statespace model of a system with input vector u, output vector y, and disturbance e takes the following form in continuous time:
$$\begin{array}{c}\frac{dx\left(t\right)}{dt}=Ax\left(t\right)+Bu\left(t\right)+Ke\left(t\right)\\ y\left(t\right)=Cx\left(t\right)+Du\left(t\right)+e\left(t\right).\end{array}$$
In discrete time, the statespace model takes the form:
$$\begin{array}{c}x\left[k+1\right]=Ax\left[k\right]+Bu\left[k\right]+Ke\left[k\right]\\ y\left[k\right]=Cx\left[k\right]+Du\left[k\right]+e\left[k\right].\end{array}$$
For idss models, the elements of the statespace matrices A, B, C, and D can be estimable parameters. The elements of the state disturbance K can also be estimable parameters. The idss model stores the values of these matrix elements in the a, b, c, d, and k properties of the model.
There are three ways to obtain an idss model.
Estimate the idss model based on inputoutput measurements of a system, using n4sid or ssest. These estimation commands estimate the values of the estimable elements of the statespace matrices. The estimated values are stored in the a, b, c, d, and k properties of the resulting idss model. The Report property of the resulting model stores information about the estimation, such as handling of initial state values and options used in estimation.
When you obtain an idss model by estimation, you can extract estimated coefficients and their uncertainties from the model using commands such as idssdata, getpar, or getcov.
Create an idss model using the idss command.
You can create an idss model to configure an initial parameterization for estimation of a statespace model to fit measured response data. When you do so, you can specify constraints on one or more of the statespace matrix elements. For example, you can fix the values of some elements, or specify minimum or maximum values for the free elements. You can then use the configured model as an input argument to an estimation command (n4sid or ssest) to estimate parameter values with those constraints.
Convert an existing dynamic system model to an idss model using the idss command.
To configure an idss model in a desired form, such as a companion or modal form, use state transformation commands such as canon and ss2ss.
A,B,C,D 
Initial values of the statespace matrices. For a system with N_{y} outputs, N_{u} inputs, and N_{x} states, specify initial values of the statespace matrix elements as follows:
Use NaN for any matrix element whose initial value is not known. 
K 
Initial value of the state disturbance matrix. Specify K as an N_{x}byN_{y} matrix. Use NaN for any matrix element whose initial value is not known. Default: N_{x}byN_{y} zero matrix. 
x0 
Initial state values. Specify the initial condition as a column vector of N_{x} values. Default: N_{x} column vector of zeros. 
Ts 
Sampling time. For continuoustime models, Ts = 0. For discretetime models, Ts is a positive scalar representing the sampling period expressed in the unit specified by the TimeUnit property of the model. To denote a discretetime model with unspecified sampling time, set Ts = 1. Default: –1 (discretetime model with unspecified sampling time) 
sys0 
Dynamic system. Any dynamic system to convert to an idss model:
For the syntax sys = idss(sys0,'split'), sys0 must be a numeric (nonidentified) tf, zpk, or ss model object. Also, sys0 must have at least as many inputs as outputs. Finally, the subsystem sys0(:,Ny+1:Ny+Nu) must contain a nonzero feedthrough term (the subsystem must be biproper). 
Specify optional commaseparated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.
Use Name,Value arguments to specify additional properties of idss models during model creation. For example, idss(A,B,C,D,'InputName','Voltage') creates an idss model with the InputName property set to Voltage.
Specify optional commaseparated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.
idss object properties include:
a,b,c,d 
Values of statespace matrices.
If you create an idss model sys using the idss command, sys.a, sys.b, sys.c, and sys.d contain the initial values of the statespace matrices that you specify with the A,B,C,D input arguments. If you obtain an idss model sys by identification using ssest or n4sid, then sys.a, sys.b, sys.c, and sys.d contain the estimated values of the matrix elements. For an idss model sys, each property sys.a, sys.b, sys.c, and sys.d is an alias to the corresponding Value entry in the Structure property of sys. For example, sys.a is an alias to the value of the property sys.Structure.a.Value. 
k 
Value of state disturbance matrix K, an N_{x}byN_{y} matrix. If you create an idss model sys using the idss command, sys.k contains the initial values of the statespace matrices that you specify with the K input argument. If you obtain an idss model sys by identification using ssest or n4sid, then sys.k contains the estimated values of the matrix elements. For an idss model sys, sys.k is an alias to the value of the property sys.Structure.k.Value. Default: N_{x}byN_{y} zero matrix. 
StateName 
State names. For firstorder models, set StateName to a string. For models with two or more states, set StateName to a cell array of strings . Use an empty string '' for unnamed states. Default: Empty string '' for all states 
StateUnit 
State units. Use StateUnit to keep track of the units each state is expressed in. For firstorder models, set StateUnit to a string. For models with two or more states, set StateUnit to a cell array of strings. StateUnit has no effect on system behavior. Default: Empty string '' for all states 
Structure 
Information about the estimable parameters of the idss model. Structure.a, Structure.b, Structure.c, Structure.d, and Structure.k contain information about the A, B, C, D, and K matrices, respectively. Each contains the following fields:

NoiseVariance 
The variance (covariance matrix) of the model innovations e. An identified model includes a white, Gaussian noise component e(t). NoiseVariance is the variance of this noise component. Typically, the model estimation function (such as ssest) determines this variance. For SISO models, NoiseVariance is a scalar. For MIMO models, NoiseVariance is a N_{y}byN_{y} matrix, where N_{y} is the number of outputs in the system. 
Report 
Information about the estimation process. Report contains the following fields:

InputDelay 
Input delay for each input channel, specified as a scalar value or numeric vector. For continuoustime systems, specify input delays in the time unit stored in the TimeUnit property. For discretetime systems, specify input delays in integer multiples of the sampling period Ts. For example, InputDelay = 3 means a delay of three sampling periods. For a system with Nu inputs, set InputDelay to an Nuby1 vector. Each entry of this vector is a numerical value that represents the input delay for the corresponding input channel. You can also set InputDelay to a scalar value to apply the same delay to all channels. Default: 0 
OutputDelay 
Output delays. For identified systems, like idss, OutputDelay is fixed to zero. 
Ts 
Sampling time. For continuoustime models, Ts = 0. For discretetime models, Ts is a positive scalar representing the sampling period expressed in the unit specified by the TimeUnit property of the model. To denote a discretetime model with unspecified sampling time, set Ts = 1. Changing this property does not discretize or resample the model. Use c2d and d2c to convert between continuous and discretetime representations. Use d2d to change the sampling time of a discretetime system. Default: –1 (discretetime model with unspecified sampling time) 
TimeUnit 
String representing the unit of the time variable. This property specifies the units for the time variable, the sampling time Ts, and any time delays in the model. Use any of the following values:
Changing this property has no effect on other properties, and therefore changes the overall system behavior. Use chgTimeUnit to convert between time units without modifying system behavior. Default: 'seconds' 
InputName 
Input channel names. Set InputName to a string for singleinput model. For a multiinput model, set InputName to a cell array of strings. Alternatively, use automatic vector expansion to assign input names for multiinput models. For example, if sys is a twoinput model, enter: sys.InputName = 'controls'; The input names automatically expand to {'controls(1)';'controls(2)'}. When you estimate a model using an iddata object, data, the software automatically sets InputName to data.InputName. You can use the shorthand notation u to refer to the InputName property. For example, sys.u is equivalent to sys.InputName. Input channel names have several uses, including:
Default: Empty string '' for all input channels 
InputUnit 
Input channel units. Use InputUnit to keep track of input signal units. For a singleinput model, set InputUnit to a string. For a multiinput model, set InputUnit to a cell array of strings. InputUnit has no effect on system behavior. Default: Empty string '' for all input channels 
InputGroup 
Input channel groups. The InputGroup property lets you assign the input channels of MIMO systems into groups and refer to each group by name. Specify input groups as a structure. In this structure, field names are the group names, and field values are the input channels belonging to each group. For example: sys.InputGroup.controls = [1 2]; sys.InputGroup.noise = [3 5]; creates input groups named controls and noise that include input channels 1, 2 and 3, 5, respectively. You can then extract the subsystem from the controls inputs to all outputs using: sys(:,'controls') Default: Struct with no fields 
OutputName 
Output channel names. Set OutputName to a string for singleoutput model. For a multioutput model, set OutputName to a cell array of strings. Alternatively, use automatic vector expansion to assign output names for multioutput models. For example, if sys is a twooutput model, enter: sys.OutputName = 'measurements'; The output names to automatically expand to {'measurements(1)';'measurements(2)'}. When you estimate a model using an iddata object, data, the software automatically sets OutputName to data.OutputName. You can use the shorthand notation y to refer to the OutputName property. For example, sys.y is equivalent to sys.OutputName. Output channel names have several uses, including:
Default: Empty string '' for all input channels 
OutputUnit 
Output channel units. Use OutputUnit to keep track of output signal units. For a singleoutput model, set OutputUnit to a string. For a multioutput model, set OutputUnit to a cell array of strings. OutputUnit has no effect on system behavior. Default: Empty string '' for all input channels 
OutputGroup 
Output channel groups. The OutputGroup property lets you assign the output channels of MIMO systems into groups and refer to each group by name. Specify output groups as a structure. In this structure, field names are the group names, and field values are the output channels belonging to each group. For example: sys.OutputGroup.temperature = [1]; sys.InputGroup.measurement = [3 5]; creates output groups named temperature and measurement that include output channels 1, and 3, 5, respectively. You can then extract the subsystem from all inputs to the measurement outputs using: sys('measurement',:) Default: Struct with no fields 
Name 
System name. Set Name to a string to label the system. Default: '' 
Notes 
Any text that you want to associate with the system. Set Notes to a string or a cell array of strings. Default: {} 
UserData 
Any type of data you wish to associate with system. Set UserData to any MATLAB^{®} data type. Default: [] 
SamplingGrid 
Sampling grid for model arrays, specified as a data structure. For arrays of identified linear (IDLTI) models that are derived by sampling one or more independent variables, this property tracks the variable values associated with each model. This information appears when you display or plot the model array. Use this information to trace results back to the independent variables. Set the field names of the data structure to the names of the sampling variables. Set the field values to the sampled variable values associated with each model in the array. All sampling variables should be numeric and scalar valued, and all arrays of sampled values should match the dimensions of the model array. For example, if you collect data at various operating points of a system, you can identify a model for each operating point separately and then stack the results together into a single system array. You can tag the individual models in the array with information regarding the operating point: nominal_engine_rpm = [1000 5000 10000];
sys.SamplingGrid = struct('rpm', nominal_engine_rpm)
where sys is an array containing three identified models obtained at rpms 1000, 5000 and 10000, respectively. Default: [] 
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