{
"title": "Multi-Rate Exact Discretization based on Diagonalization of a Linear System - A Multiple-Real-Eigenvalue Case",
"authors": "T. Sakamoto, N. Hori",
"country": null,
"institution": null,
"volume": "62",
"journal": "International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering",
"pagesStart": 172,
"pagesEnd": 177,
"ISSN": "1307-6892",
"URL": "http:\/\/waset.org\/publications\/11989",
"abstract": "A multi-rate discrete-time model, whose response\nagrees exactly with that of a continuous-time original at all sampling\ninstants for any sampling periods, is developed for a linear system,\nwhich is assumed to have multiple real eigenvalues. The sampling\nrates can be chosen arbitrarily and individually, so that their ratios\ncan even be irrational. The state space model is obtained as a\ncombination of a linear diagonal state equation and a nonlinear output\nequation. Unlike the usual lifted model, the order of the proposed\nmodel is the same as the number of sampling rates, which is less than\nor equal to the order of the original continuous-time system. The\nmethod is based on a nonlinear variable transformation, which can be\nconsidered as a generalization of linear similarity transformation,\nwhich cannot be applied to systems with multiple eigenvalues in\ngeneral. An example and its simulation result show that the proposed\nmulti-rate model gives exact responses at all sampling instants.",
"references": null,
"publisher": "World Academy of Science, Engineering and Technology",
"index": "International Science Index 62, 2012"
}