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Mathematica > Mathematics and Algorithms > Control Systems > Basic Modeling > DualSystemsModel >

BUILT-IN MATHEMATICA SYMBOL

DualSystemsModel

DualSystemsModel[ss]
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 dual of a system:

Out[1]=

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: