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You can estimate statespace models in two ways at the command line, depending upon your prior knowledge of the nature of the system and your requirements.
In this approach, you specify the model order, and, optionally, additional model structure attributes that configure the overall structure of the statespace matrices. You call ssest, ssregest or n4sid with data and model order as primary input arguments, and use namevalue pairs to specify any additional attributes, such as model sample time, presence of feedthrough, absence of noise component, etc. You do not work directly with the coefficients of the A, B, C, D, K, and X0 matrices.
In this approach, you create and configure an idss model that contains the initial values for all the system matrices. You use the Structure property of the idss model to specify all the parameter constraints. For example, you can designate certain coefficients of system matrices as fixed and impose minimum/maximum bounds on the values of the others. For quick configuration of the parameterization and whether to estimate feedthrough and disturbance dynamics, use ssform.
After configuring the idss model with desired constraints, you specify this model as an input argument to the ssest command. You cannot use n4sid or ssregest for structured estimation.
Note:

You can estimate continuoustime and discretetime statespace models using the iterative estimation command ssest that minimizes the prediction errors to obtain maximumlikelihood values.
Use the following general syntax to both configure and estimate statespace models:
m = ssest(data,n,opt,Name,Value)
where data is the estimation data, n is the model order. opt contains the options for configuring the estimation of the statespace models. These options include the handling of the initial conditions, input and output offsets, estimation focus and search algorithm options. opt can be followed by name and value pair input arguments that specify optional model structure attributes such as the presence of feedthrough, the canonical form of the model, and input delay.
As an alternative to ssest, you can use the noniterative subspace estimators n4sid or ssregest:
m = n4sid(data,n,opt,Name,Value) m = ssregest(data,n,opt,Name,Value)
Unless you specify the sample time as a namevalue pair input argument, n4sid and ssregest estimate a discretetime model, while ssest estimates a continuoustime model.
Note: ssest uses n4sid to initialize the statespace matrices, and takes longer than n4sid to estimate a model but typically provides better fit to data. 
For information about validating your model, see Validating Models After Estimation
By default, all entries of the A, B, and C statespace matrices are treated as free parameters. Using the Form name and value pair input argument of ssest , you can choose various canonical forms, such as the companion and modal forms, that use fewer parameters.
For more information about estimating a specific statespace parameterization, see:
For estimation of statespace models, you have the option of switching the model sample time between zero and that of the estimation data. You can do this using the Ts name and value pair input argument.
By default, ssest estimates a continuoustime model. If you are using data set with nonzero sample time, data, which includes all time domain data, you can also estimate a discretetime model by using:
model = ssest(data,nx,'Ts',data.Ts);
If you are using continuoustime frequencydomain data, you cannot estimate a discretetime model.
By default, n4sid and ssregest estimate a model whose sample time matches that of the data. Thus, for timedomain data, n4sid and ssregest deliver a discretetime model. You can estimate a continuoustime model by using:
model = n4sid(data,nx,'Ts',0);
or
model = ssregest(data,nx,'Ts',0);
For statespace models with any parameterization, you can specify whether to estimate the D, K and X0 matrices, which represent the inputtooutput feedthrough, noise model and the initial states, respectively.
For statespace models with structured parameterization, you can also specify to estimate the D matrix. However, for free and canonical forms, the structure of the D matrix is set based on your choice of 'Feedthrough' name and value pair input argument.
By default, the D matrix is not estimated and its value is fixed to zero, except for static models.
Black box estimation: Use the Feedthrough name and value pair input argument to denote the presence or absence of feedthrough from individual inputs. For example, in case of a two input model such that there is feedthrough from only the second input, use model = n4sid(data,n,'Feedthrough',[false true]);.
Structured estimation: Configure the values of the init_sys.Structure.d, where init_sys is an idss model that represents the desired model structure. To force no feedthrough for the ith input, set:
init_sys.Structure.d.Value(:,i) = 0; init_sys.Structure.d.Free = true; init_sys.Structure.d.Free(:,i) = false;
The first line specifies the value of the ith column of D as zero. The next line specifies all the elements of D as free, estimable parameters. The last line specifies that the ith column of the D matrix is fixed for estimation.
Alternatively, use ssform with 'Feedthrough' namevalue pair..
K represents the noise matrix of the model, such that the noise component of the model is:.
For frequencydomain data, no noise model is estimated and K is set to 0. For timedomain data, K is estimated by default in the black box estimation setup. y^{n} is the contribution of the disturbances to the model output.
Black box estimation: Use the DisturbanceModel name and value pair input argument to indicate if the disturbance component is fixed to zero (specify Value = ‘none') or estimated as a free parameter (specify Value = ‘estimate'). For example, use model = n4sid(data,n,'DisturbanceModel','none').
Structured estimation: Configure the value of the init_sys.Structure.k parameter, where init_sys is an idss model that represents the desired model structure. You can fix some K matrix coefficients to known values and prescribe minimum/maximum bounds for free coefficients. For example, to estimate only the first column of the K matrix for a two output model:
kpar = init_sys.Structure.k; kpar.Free(:,1) = true; kpar.Free(:,2) = false; kpar.Value(:,2) = 0; % second column value is fixed to zero init_sys.Structure.k = kpar;
Alternatively, use ssform.
When not sure how to easily fix or free all coefficients of K, initially you can omit estimating the noise parameters in K to focus on achieving a reasonable model for the system dynamics. After estimating the dynamic model, you can use ssest to refine the model while configuring the K parameters to be free. For example:
init_sys = ssest(data, n,'DisturbanceModel','none'); init_sys.Structure.k.Free = true; sys = ssest(data, init_sys);
where init_sys is the dynamic model without noise.
To set K to zero in an existing model, you can set its Value to 0 and Free flag to false:
m.Structure.k.Value = 0; m.Structure.k.Free = false;
The initial state vector X0 is obtained as the byproduct of model estimation. The n4sid, ssest and ssregest commands return the value of X0 as their second output arguments. You can choose how to handle initial conditions during model estimation by using the InitialState estimation option. Use n4sidOptions (for n4sid), ssestOptions (for ssest) or ssregestOptions (for ssregest) to create the estimation option set. For example, in order to hold the initial states to zero during estimation using n4sid:
opt = n4sidOptions; opt.InitialState = 'zero'; [m,X0] = n4sid(data,n,opt);
The returned X0 variable is a zero vector of length n.
When you estimate models using multiexperiment data, the X0 matrix contains as many columns as data experiments.
For a complete list of values for the InitialStates option, see Specifying Initial States for Iterative Estimation Algorithms.