gives the dual of the state-space model ssm.


  • The state-space model ssm can be a standard or descriptor StateSpaceModel.
  • The original and dual systems for a standard StateSpaceModel[{a,b,c,d}]:
  • The original and dual systems for a descriptor StateSpaceModel[{a,b,c,d,e}]:


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Basic Examples  (1)

The dual of a system:

Scope  (3)

A dual model:

All variables are considered as complex:

Simplify, assuming all variables are real:

Specify only some variables to be real:

The dual of a descriptor system:

Properties & Relations  (4)

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:

Introduced in 2010
Updated in 2012