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State-Space Models

State-space representations of LTI models

The representation of a model in state-space is not unique. Coordinate transformation yields state-space models with different matrices but identical dynamics. State coordinate transformation can be useful for achieving minimal realizations of state-space models, or for converting canonical forms for analysis and control design.

Coordinate transformation can also be useful for scaling poorly-conditioned models. Proper scaling of state-space models is important for accurate computations. An example of a poorly scaled model is a dynamic system with two states in the state vector that have units of light years and millimeters. Such disparate units may introduce both very large and very small entries into the A matrix. Over the course of computations, this mix of small and large entries in the matrix could destroy important characteristics of the model and lead to incorrect results.


balrealBalanced state-space realization
prescaleOptimal scaling of state-space models
modalrealCompute modal state-space realization (Since R2023b)
comprealCompute companion state-space realization (Since R2023b)
ss2ssState coordinate transformation for state-space model
ssequivEquivalence transformation for state-space models (Since R2023b)
xperm Reorder states in state-space models
xsortSort states based on state partition (Since R2020b)
xelimEliminate states from state-space models (Since R2023b)
augstateAppend state vector to output vector
ctrbControllability of state-space model
obsvObservability of state-space model
gramControllability and observability Gramians
augoffsetMap offset contribution to extra input channel (Since R2024a)
dss2ssConvert descriptor state-space model to explicit form (Since R2024a)
fixInput Fix value of some inputs and delete them (Since R2024a)