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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
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