Invert the descriptor matrix to create a standard state-space model:

Add an identity matrix to create a descriptor form:

Obtain the descriptor StateSpaceModel:

By default, the standard form is obtained:

For some singular systems, the descriptor form is obtained by default:

This is because it is not possible to obtain the standard form:

When possible, the standard form is obtained:

The descriptor form:

In some cases, the standard form can have fewer states:

However, the order of the system is the same in both cases:

Obtain the result from StateSpaceTransform in the descriptor form:

By default, the form is unaltered:

Create a standard state-space model from a descriptor state-space model:

Create a descriptor state-space model from a standard state-space model:

Convert a proper transfer-function model to a descriptor state-space model:

Create a descriptor state-space model from an ODE:

Obtain the state transformation of a standard StateSpaceModel in descriptor form:

It gives the same result as an explicit descriptor specification:

Similar results can be obtained with the inverse transformation as well:

A descriptor StateSpaceModel with an invertible descriptor matrix:

Its state transformation can be obtained in standard form:

Improper transfer-function models will create descriptor state-space models by default:

There is no standard state-space realization:

A descriptor StateSpaceModel with a noninvertible descriptor matrix:

StateSpaceTransform produces a descriptor model:

The state transformation cannot be obtained in standard form: