gives the minimal state-space model of the state-space model sys.
specifies the new coordinates zi.
Details and Options
- The minimal state-space model is both controllable and observable, and has the minimal number of states.
- The system sys can be a standard or descriptor StateSpaceModel or AffineStateSpaceModel.
Examplesopen allclose all
Obtain a model with the minimal number of states:
A minimal realization of a symbolic model:
A minimal realization does not contain uncontrollable modes:
A minimal realization does not contain unobservable modes:
The minimal realization of a descriptor system:
The minimal realization of an affine system:
Remove any uncontrollable or unobservable modes:
A parallel mass-spring-damper system is not completely controllable and observable. Design a controller based on the minimal system:
Design a controller based on the minimal system:
Simulate the response of the closed-loop system and compare it with the open-loop system:
Properties & Relations (4)
MinimalStateSpaceModel computes the subspace that is both controllable and observable:
A minimal realization is both controllable and observable:
Minimal realizations are not unique:
Both are minimal realizations of the same transfer function:
MinimalStateSpaceModel is equivalent to TransferFunctionCancel for scalar systems:
Wolfram Research (2010), MinimalStateSpaceModel, Wolfram Language function, https://reference.wolfram.com/language/ref/MinimalStateSpaceModel.html (updated 2014).
Wolfram Language. 2010. "MinimalStateSpaceModel." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/MinimalStateSpaceModel.html.
Wolfram Language. (2010). MinimalStateSpaceModel. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MinimalStateSpaceModel.html