@article{(Open Science Index):https://publications.waset.org/pdf/11989,
	  title     = {Multi-Rate Exact Discretization based on Diagonalization of a Linear System - A Multiple-Real-Eigenvalue Case},
	  author    = {T. Sakamoto and  N. Hori},
	  country	= {},
	  institution	= {},
	  abstract     = {A multi-rate discrete-time model, whose response
agrees exactly with that of a continuous-time original at all sampling
instants for any sampling periods, is developed for a linear system,
which is assumed to have multiple real eigenvalues. The sampling
rates can be chosen arbitrarily and individually, so that their ratios
can even be irrational. The state space model is obtained as a
combination of a linear diagonal state equation and a nonlinear output
equation. Unlike the usual lifted model, the order of the proposed
model is the same as the number of sampling rates, which is less than
or equal to the order of the original continuous-time system. The
method is based on a nonlinear variable transformation, which can be
considered as a generalization of linear similarity transformation,
which cannot be applied to systems with multiple eigenvalues in
general. An example and its simulation result show that the proposed
multi-rate model gives exact responses at all sampling instants.},
	    journal   = {International Journal of Mathematical and Computational Sciences},
	  volume    = {6},
	  number    = {2},
	  year      = {2012},
	  pages     = {172 - 176},
	  ee        = {https://publications.waset.org/pdf/11989},
	  url   	= {https://publications.waset.org/vol/62},
	  bibsource = {https://publications.waset.org/},
	  issn  	= {eISSN: 1307-6892},
	  publisher = {World Academy of Science, Engineering and Technology},
	  index 	= {Open Science Index 62, 2012},
	}