This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)


gives the dual of the StateSpaceModel object ss.
  • The state-space model ss can be given as StateSpaceModel, where a, b, c, and d represent the state, input, output, and transmission matrices in either a continuous-time or a discrete-time system.
  • The models and their duals:
The dual of a system:
The dual of a system:
Click for copyable input
A dual model:
All variables are considered as complex:
Simplify assuming all variables are real:
Specify only some variables to be real:
The controllable and observable realizations have a dual relationship:
A similar relationship exists between the controllable companion and observable companion forms:
An uncontrollable but observable model:
The dual model is controllable but not observable:
The controllability matrix of a system is the conjugate transpose of the observability matrix of the dual system and vice versa:
The estimator gains are the conjugate transpose of feedback gains of the dual model and vice versa:
New in 8