System Identification Toolbox™ software supports the following parameterizations that indicate which parameters are estimated and which remain fixed at specific values:
Free parameterization results in the estimation of all elements of the system matrices A, B, C, D, and K. See Estimate State-Space Models with Free-Parameterization.
Canonical parameterization represents a state-space system in a reduced-parameter form where many entries of the A, B and C matrices are fixed to zeros and ones. The free parameters appear in only a few of the rows and columns in the system matrices A, B, C and D. The software supports companion, modal decomposition and observability canonical forms. See Estimate State-Space Models with Canonical Parameterization.
Structured parameterization lets you specify the fixed values of specific parameters and exclude these parameters from estimation. You choose which entries of the system matrices to estimate and which to treat as fixed. See Estimate State-Space Models with Structured Parameterization.
Completely arbitrary mapping of parameters to state-space matrices. See Estimating Linear Grey-Box Models.