Affine LPV systems: realization theory, input-output equations and relationship with linear switched systems
Abstract
We formulate a Kalman-style realization theory for discrete-time affine LPV systems. By an affine LPV system we mean an LPV system whose matrices are affine functions of the scheduling parameter. In this paper we characterize those input-output behaviors which exactly correspond to affine LPV systems. In addition, we characterize minimal affine LPV systems which realize a given input-output behavior. Furthermore, we explain the relationship between Markov-parameters, Hankel-matrices, existence of an affine LPV realization and minimality. The results are derived by reducing the problem to the realization problem for linear switched systems. In this way, as a secondary contribution, we formally demonstrate the close relationship between LPV systems and linear switched systems. In addition we show that an input-output map has a realization by an affine LPV system if and only if it satisfies certain types of input-output equations.
Keywords
Cite
@article{arxiv.1209.0345,
title = {Affine LPV systems: realization theory, input-output equations and relationship with linear switched systems},
author = {Mihaly Petreczky and Guillaume Mercère and Roland Tóth},
journal= {arXiv preprint arXiv:1209.0345},
year = {2013}
}
Comments
This paper is an extended version of Mih\'aly Petreczky, Guillaume Merc\`ere: Affine LPV systems: Realization theory, input-output equations and relationship with linear switched systems. CDC 2012: 4511-4516. 2012. The main difference with respect to the previous version is that some errors have been corrected, proofs and explanation were added. arXiv admin note: text overlap with arXiv:1103.1343 by other authors