# State-Space Model Analysis VIs

LabVIEW 2018 Control Design and Simulation Module Help

Edition Date: March 2018

Part Number: 371894J-01

»View Product Info

Owning Palette: Control Design VIs and Functions

Requires: Control Design and Simulation Module. This topic might not match its corresponding palette in LabVIEW depending on your operating system, licensed product(s), and target.

Use State-Space Model Analysis VIs to calculate properties of a given state-space model, such as observability, detectability, controllability, stabilizability, similarity transformations, model balance, and system Grammians.

The State-Space Model Analysis VIs do not support the Stochastic Systems VIs.

The VIs on this palette can return general LabVIEW error codes or specific control design error codes.

Palette ObjectDescription
CD Balance State-Space Model (Diagonal)Balances the State-Space Model using a diagonal similarity transformation. This transformation reduces the ratios of rows and columns norms of the system matrix A, or of the matrix S defined by the following equation.

S = [A B| C 0]
CD Balance State-Space Model (Grammians)Calculates a Balanced State-Space Model based on Grammians. The resulting balanced transformation has identical controllability and observability diagonal Grammians.
CD Canonical State-Space RealizationTransforms the State-Space Model to a canonical form that Form Type specifies. This VI also returns the similarity Transformation Matrix that this VI uses to transform the given system.
CD Controllability MatrixCalculates the Controllability Matrix of the State-Space Model. You can use the controllability matrix Q to determine if the given system is controllable. A system of order n is controllable if Q is full rank, meaning the rank of Q is equal to n. This VI also determines if the given system is stabilizable. A system is stabilizable if all the unstable eigenvalues are controllable.
CD Controllability StaircaseCalculates the controllable staircase similarity transformation of the State-Space Model. You can use the staircase representation to identify controllable and uncontrollable states by simple inspection of the A and B matrices of the transformed model.
CD GrammiansCalculates the controllability or observability Grammian of the State-Space Model for a stable system. The system can be continuous or discrete. You can use this VI to balance state-space models and to study controllability and observability properties of the system.
CD Observability MatrixCalculates the Observability Matrix of the State-Space Model. You can use the observability matrix N to determine if the given system is observable. A system of order n is observable if N is full rank, meaning the rank of N is equal to n. This VI also determines if the given system is detectable. A system is detectable if all the unstable eigenvalues are observable.
CD Observability StaircaseCalculates the observable staircase similarity transformation of a State-Space Model. You can use the staircase representation to identify observable and unobservable states by simple inspection of the A and C matrices of the transformed model.
CD Similar State-Space ModelsCompares two state-space models and determines if the models are equal (with the same A, B, C, and D values) or similar.

Two state-space models are similar if you can use a similarity transformation matrix to transform the states of one model into the states of the other model linearly and within a certain tolerance.
CD State Similarity TransformApplies a similarity transformation on State-Space Model using the given Transformation Matrix (T).

Not Helpful