The trouble with imaginary eigenvalues. Optimal control, controllability, frequency response
Optimization and Control
2022-02-01 v2
Abstract
We investigate a few problems in the theory of linear time-invariant systems that arise when the open-loop system possesses imaginary eigenvalues. The problems are: (1) the infinite horizon, minimum energy optimal control problem; (2) the matter of defining the controllability Gramian for systems that are not stable; (3) the regularity as a distribution of the Fourier transform of the state impulse response. Apart from separately investigating these problems, we also indicate how they are interconnected.
Keywords
Cite
@article{arxiv.2003.04374,
title = {The trouble with imaginary eigenvalues. Optimal control, controllability, frequency response},
author = {Bahman Gharesifard and Andrew D. Lewis},
journal= {arXiv preprint arXiv:2003.04374},
year = {2022}
}
Comments
There is an error in the manner in which the stabilising feedback is implemented in the case of multiple canonical blocks