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State-Coordinate Transformation

Coordinate transformation for state-space 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.


balrealGramian-based input/output balancing of state-space realizations
canonCanonical state-space realization
prescaleOptimal scaling of state-space models
ss2ssState coordinate transformation for state-space model
xperm Reorder states in state-space models