gives the order of the state-space model sys.


  • The system sys can be a standard or descriptor StateSpaceModel, an AffineStateSpaceModel, or a NonlinearStateSpaceModel, all with no delays.
  • The order of a standard continuous-time systems model is the number of integrators in the model and for standard discrete-time systems, the number of integer delays in the model.
  • For a descriptor StateSpaceModel, the order is taken to be the dimension of the slow subsystem.


open allclose all

Basic Examples  (2)

The order of a state-space model:

The order of a descriptor state-space model:

It can be computed as the exponent of the polynomial Det[s e-a]:

Scope  (6)

A standard state-space model:

A nonsingular descriptor state-space model:

A singular descriptor state-space model:

A discrete-time system with integer time delay:

An affine state-space model:

A nonlinear state-space model:

Applications  (2)

Use SystemsModelOrder and ControllableDecomposition to test for controllability:

Test for observability:

Properties & Relations  (3)

The order of a singular state-space model depends on the descriptor matrix:

The order is equivalent to the exponent of the polynomial Det[s e-a]:

It also equals the size of the slow system found with KroneckerModelDecomposition:

The slow system size is shown by the number of ones on the descriptor matrix diagonal:

The order of a discrete-time time-delay system is the total number of delays in the system:

The order of a system with no zero dynamics is the total of the vector relative orders:

Use SystemsModelVectorRelativeOrders to get the relative orders:

Possible Issues  (1)

Discrete-time systems with fractional delays are not supported:

Approximate the delays:

Wolfram Research (2010), SystemsModelOrder, Wolfram Language function, (updated 2014).


Wolfram Research (2010), SystemsModelOrder, Wolfram Language function, (updated 2014).


Wolfram Language. 2010. "SystemsModelOrder." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014.


Wolfram Language. (2010). SystemsModelOrder. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_systemsmodelorder, author="Wolfram Research", title="{SystemsModelOrder}", year="2014", howpublished="\url{}", note=[Accessed: 15-June-2024 ]}


@online{reference.wolfram_2024_systemsmodelorder, organization={Wolfram Research}, title={SystemsModelOrder}, year={2014}, url={}, note=[Accessed: 15-June-2024 ]}