Analysis of State-Space Models

Mathematica 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

ControllabilityMatrix — gives the controllability matrix

ControllabilityGramian — gives the controllability Gramian

ControllableModelQ — tests whether a model is controllable

OutputControllabilityMatrix — gives the output controllability matrix

OutputControllableModelQ — tests whether a model is output controllable

ObservabilityMatrix — gives the observability matrix

ObservabilityGramian — gives the observability Gramian

ObservableModelQ — tests whether a model is observable

State-Space Decompositions

ControllableDecomposition — gives the controllable subspace

ObservableDecomposition — gives the observable subspace

MinimalStateSpaceModel — gives the subspace that is controllable and observable

InternallyBalancedDecomposition — balances state controllability and observability

JordanModelDecomposition — gives the Jordan canonical form

MORE ABOUT