Solutions of differential-algebraic equations as outputs of LTI systems: application to LQ control problem
Abstract
In this paper we synthesize behavioral ideas with geometric control theory and propose a unified geometric framework for representing all solutions of a Linear Time Invariant Differential-Algebraic Equation (DAE-LTI) as outputs of classical Linear Time Invariant systems (ODE-LTI). An algorithm for computing an ODE-LTI that generates solutions of a given DAE-LTI is described. It is shown that two different ODE-LTIs which represent the same DAE-LTI are feedback equivalent. The proposed framework is then used to solve an LQ optimal control problem for DAE-LTIs with rectangular matrices.
Keywords
Cite
@article{arxiv.1312.7547,
title = {Solutions of differential-algebraic equations as outputs of LTI systems: application to LQ control problem},
author = {Mihaly Petreczky and Sergiy Zhuk},
journal= {arXiv preprint arXiv:1312.7547},
year = {2016}
}
Comments
The main difference with respect to the previous version is that the supplementary files were included which were missing from the previous version. Note that part of the material of this report appeared in arXiv:1309.1235. A version of this paper was submitted to Automatica, first in January 2014 and then in November 2014, and then in November 2015