Takashi Sakamoto and Noriyuki Hori
Diagonalization, discretization, linear systems, multi-rate state sampling, nonlinear transformation, similarity transformation
The present paper shows that multi-rate exact discretization of states can be modelled efficiently for a linear system with distinct real eigenvalues by transforming it into a diagonal system with non-zero but otherwise arbitrary, real eigenvalues. The diagonalization can be carried out using a variable transformation, which is found as a solution to an associated partial differential equation. The resulting transformation is nonlinear when the eigenvalues are to be modified and is linear when the eigenvalues remain the same, which corresponds to the well-known similarity transformation. The inverse transformation can always be found by properly choosing the design parameters. The method is applied to multi-rate exact discretization such that the discrete-time model is obtained as a linear state-space equation with a nonlinear output equation.
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