Analysis of State-Space Models

The Wolfram Language provides a complete set of functions needed to compute and verify the controllability and observability properties of linear systems, as well as advanced functions that yield decompositions with desired controllability and observability characteristics.

Controllability and Observability Properties

(RefLink[ControllableModelQ, paclet:ref/ControllableModelQ]) — test whether the states are controllable from the inputs

(RefLink[ObservableModelQ, paclet:ref/ObservableModelQ]) — test whether the states are observable from outputs

Controllability and Observability Transformations

(RefLink[MinimalStateSpaceModel, paclet:ref/MinimalStateSpaceModel]) — give the subsystem that is controllable and observable

(RefLink[InternallyBalancedDecomposition, paclet:ref/InternallyBalancedDecomposition]) — balance state controllability and observability

General Transformations

(RefLink[StateSpaceTransform, paclet:ref/StateSpaceTransform]) — coordinate transformation of the states of a model

(RefLink[JordanModelDecomposition, paclet:ref/JordanModelDecomposition]) — transform state matrix to Jordan form

(RefLink[KroneckerModelDecomposition, paclet:ref/KroneckerModelDecomposition]) — decouple fast and slow subsystems