| Creating and Manipulating Models | |
State-Space Realizations
The following functions are useful to analyze, perform state coordinate transformations on, and derive canonical state-space realizations for single state-space LTI models or LTI arrays of state-space models.
| State-Space Realizations | |
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Canonical state-space realizations. |
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Controllability matrix. |
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Controllability staircase form. |
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Controllability and observability gramians. |
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Observability matrix. |
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Observability staircase form. |
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State coordinate transformation. |
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Diagonal balancing of state-space realizations. |
The function ssbal uses a simple diagonal similarity transformation
to balance the state-space data 
. This is accomplished by reducing the norm of the matrix.
Such balancing usually improves the numerical conditioning of subsequent state-space computations. Note that conversions to state-space using ss produce balanced realizations of transfer functions and zero-pole-gain models.
By contrast, the canonical realizations produced by canon, ctrbf, or obsvf are often badly scaled, sensitive to perturbations of the data, and poorly suited for state-space computations. Consequently, it is wise to use them only for analysis purposes and not in control design algorithms.
| | Model Dynamics | Arrays of LTI Models | |